The solubilities of phosphate and sulfate salts in supercritical ... - ITM

J. of Supercritical Fluids 54 (2010) 1–8
Contents lists available at ScienceDirect
The Journal of Supercritical Fluids
journal homepage: www.elsevier.com/locate/supflu
The solubilities of phosphate and sulfate salts in supercritical water
Ingo Leusbrock a,∗ , Sybrand J. Metz a , Glenn Rexwinkel b , Geert F. Versteeg b,c
a Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8900 CC Leeuwarden, The Netherlands
b PROCEDE TWENTE B.V., 7500 AH Enschede, The Netherlands
c University of Groningen, Institute of Technology, Engineering and Management - Centre of Natural Sciences and Technology, 9747 AG Groningen, The Netherlands
article
info
abstract
Article history:
Received 19 January 2010
Received in revised form 7 March 2010
Accepted 8 March 2010
Keywords:
Phosphates
Solubility
Sulfates
Supercritical water
Inorganic compounds are regularly present in aqueous streams. To understand their influence and behavior
on these streams at supercritical conditions, little to no property data is available, which can be used
as starting point for further research or application design. Since inorganic compounds tend to precipitate
at these conditions, scaling, blocking and erosion can occur as a consequence. Furthermore, a separation
of (precious) compounds from the bulk stream due to the precipitation is possible. Here, phosphate compounds
are regarded as interesting for further investigation since resources are assumed to be depleted
in future. As phosphate is present in many waste streams, these could be used as sources for recoverable
phosphate. Resulting from these facts and options, a proper understanding and knowledge of these systems
is important for later industrial applications. Therefore, the authors have investigated the behavior
of salts (e.g. NaCl, NaNO 3 and MgCl 2 ) in supercritical water in previous works.
To extend this knowledge, the solubilities of the sulfate salts MgSO 4 and CaSO 4 in a range of
18.8–23.2 MPa and 655–675 K as well as of the phosphate salts Na 2 HPO 4 , NaH 2 PO 4 and CaHPO 4 in a
range of 20.5–24.2 MPa and 665–690 K were investigated in this work with a continuous flow method
in continuation of former work of the authors. The solubilities were compared with existing data available
from open literature. A quantitative correlation on base of a phase equilibrium between the present
phases was used to describe the behavior and to compare it with previous results. For the investigated
calcium salts, CaSO 4 and CaHPO 4 , it was found that a significant solubility decrease already happens at
subcritical conditions resulting in precipitation in unwanted locations. For the remaining compounds, a
parallel hydrolysis reaction was found as could be seen from a change in pH in the effluent stream.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
Supercritical water (SCW) is regarded as one of the most promising
and interesting solvents/environments for future industrial
applications such as hydrothermal conversion of biomass [1,2],
destruction of waste sludge and organic waste compounds [3,4],
particle formation on a micro- and nanoscale [5,6], reaction media
for polymerizations and conversion processes [7,8] and separation
of inorganic compounds. Due to fundamental changes in properties
at supercritical conditions (critical temperature T c = 647 K, critical
pressure p c = 22.1 MPa), SCW varies to a large degree in its
properties compared to the common phases liquid and vapor. The
additional benefit of supercritical fluids and SCW is the fact that
properties like diffusion rate, density and viscosity are adjustable in
the supercritical regime [9,10]. As a result of the comparably harsh
critical conditions of water 1 and a limited number of industrial
and commercial installations, available property data on systems
containing supercritical water is scarce in comparison to other
supercritical fluids.
Inorganic compounds can be found in a majority of aqueous
streams. At supercritical conditions, these compounds tend to precipitate
or to form vapor or liquid phases saturated in salt. This
precipitation can lead to scaling and plugging in installations and
therefore has to be controlled or avoided [11,12]. First investigated
in connection with supercritical water oxidation (SCWO) [13,14],it
became obvious in later applications like supercritical water gasification
(SCWG) that the presence of inorganic compounds can have
a major influence on the reaction and the process itself (e.g. as a
catalyst [15]). Furthermore, severe problems can occur for a continuous
long-term process (e.g. corrosion [16,17], increased pressure
drops due to scaling [12], catalyst poisoning [18]). Therefore, concepts
were developed to avoid the formation of such a solid phase
∗ Corresponding author. Tel.: +31 58 2843000; fax: +31 58 2843001.
E-mail address: ingo.leusbrock@wetsus.nl (I. Leusbrock).
URL: http://www.wetsus.nl (I. Leusbrock).
1 Carbon dioxide as the most frequently applied supercritical fluid has a critical
temperature T c = 304 K and a critical pressure p c = 7.4 MPa.
0896-8446/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.supflu.2010.03.003

2 I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8
Fig. 1. Scheme of the experimental setup.
(e.g. different reactor modifications [19,20]) or to separate inorganic
compounds in an integrated treatment step before the actual
process step [18,21]. For the design of these new concepts and even
more sophisticated ones like a fractionization of different salt fractions,
it is vital to have a sound understanding of the solubility
of these inorganic compounds and their influence and behavior.
One of the group of compounds, which are of interest for a separation
from other compounds, are phosphates. Phosphates are part
of many waste streams, which represents a potential source for
recoverable phosphate [22]. As phosphate resources are limited
and a shortage or even a depletion of global resources is expected,
new ways have to be found to recover phosphate and to guarantee
sufficient fertilizers for global food production.
In previous works of the authors, monovalent salts (alkali
nitrates and chlorides [23,24]) and bivalent salts (calcium and
magnesium chloride [25]) were investigated. Here, a continuous
flow method was used to investigate the solubilities of these
compounds. In these studies, different quantitative approaches to
describe solubilities in SCW were compared. The behavior and a
quantitative description for the solubility of monovalent chloride
and nitrate salts and double-valent chloride salts was presented.
In the course of this study, the solubilities and behavior of the
bivalent salts MgSO 4 and CaSO 4 in a range of 18.8–23.2 MPa and
655–675 K as well as of the mono-/bivalent cation/triple-valent
anion phosphate salts Na 2 HPO 4 , NaH 2 PO 4 and CaHPO 4 in a range
of 20.5–24.2 MPa and 665–690 K was object of the investigations.
The experimental data was correlated with an approach derived in
an earlier work [23]. The results of this correlation are compared
with previous results of the authors as well as with data of similar
compounds available in literature [26].
2. Theoretical background
2.1. Correlation of the experimental data
For quantitative description of the solubilities, an approach on
base of a phase equilibrium between the present phases is applied
[23,27]. In this approach, the solid phase and the supercritical fluid
are assumed to form an equilibrium depending on the conditions in
the system [23]. Thereby, a description of the equilibrium between
the phases is possible in the following manner:
a · Me c × m · H 2 O(f ) + b · X d × p · H 2 O(f ) ⇋ Me a X b × n · H 2 O(f )
Me a X b × n · H 2 O(f ) ⇋ Me a X b (s) + n · H 2 O(f )
⇒ K s = ˛Me aX b ×n·H 2 O(f )
·˛MeaX b (s)˛n
H 2 O(f )
Me and X resemble the salt cation/the salt anion; a and b is the
number of ions in the salt molecule; c and d their valency; s and
f refer to the solid and fluid phase; n, m and p to the number of
water molecules. For this approach it is furthermore assumed that
a formation of the solid phase occurs via the associated complex and
not directly via dissociated ions [28]. For the equilibrium constant
K s , several simplifications can be made. Interaction between the
species in the system is neglected; the activity coefficient of the
solid phase is assumed as unity. The fluid phase is treated as an
ideal one. A more extensive description of this approach can be
found be elsewhere [23,24,27]. As a result of these assumptions,
the solubility of inorganic compounds in supercritical water can be
(1)

I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8 3
described in the following way:
K ∗ s ≈ m Me aX b ×n·H 2 O(f )
1 · n m,H 2 O(f )
(2)
⇒ m MeaX b ×n·H 2 O(f ) = K ∗ s · n m, H 2 O(f )
Substituting the equilibrium constant under usage of a van’t
Hoff-like expression leads to the following expression:
K ∗ s ≈ m Me aX b ×n·H 2 O(f )
1 · n m, H 2 O(f )
⇒ log m MeaX b ×n·H 2 O
⇒ m MeaX b ×n·H 2 O(f ) = K ∗ s · n m, H 2 O(f )
= log Ks ∗ + n · log m, H 2 O
=− solvH
R · T
+ solvS
+ n · log m, H2 O
R
For a more convenient interpretation of the parameters, a
description on an amount of substance base is chosen. K s and K ∗ s
are the equilibrium constant and the equilibrium constant including
the simplifications. R is the universal gas constant, T the system
temperature, m the molality, the density, n the coordination
number. The Gibbs energy of solvation, solv G, the enthalpy of solvation,
solv H, and the entropy of solvation, solv S are assumed as
independent of the system parameters temperature, pressure and
density. The density of pure water is calculated via the IAPWS95
equation of state [29]. Experimental data was fitted to the parameters
solv H, solv S and n to quantitatively describe the solubility. A
more detailed description on this approach can be found elsewhere
[23,24].
3. Experimental
For the measurements of the solubilities of the phosphate and
sulfate salts, a continuous flow method was applied like in the
previous works of the authors. The most important details of the
method and setup are presented in the following; a more detailed
description can be found elsewhere [23,24].
The setup is designed for an operation up to 25 MPa and 723 K.
A scheme of the setup can be found in Fig. 1. Heat was provided by
a custom-made oven and a pre-heater; for pressurization and flow,
a HPLC Pump was used (LabAlliance Series III, LabAlliance, USA). An
U-tube was installed inside the oven with a length of 265 mm, an
inner diameter of 4.6 mm and an outer diameter of 6.35 mm. The
temperature inside the oven was measured at inlet, middle and outlet
position by standard Type K thermocouples (relative uncertainty
0.25%). The pressure inside the setup is measured with a pressure
sensor (Keller PA23H, relative uncertainty 0.2%). The material of
choice for all heated parts was Hastelloy, the diameter of every
tubing was 1/16 ′′ (= 1.588 mm) if not mentioned otherwise.
The feed stream enters the U-tube, where an oversaturation
of the feed stream depending on the system conditions (pressure,
temperature, and density) and the feed concentration can
occur. If so, the exceeding amount starts to precipitate and form
an additional phase till an equilibrium in the system has established.
The stream exits the U-tube at an equilibrium state with
a composition resulting from the system conditions. After cooling
and depressurization, samples can be taken. The analysis of
these samples is done via an inductive coupled plasma atom emission
spectrometer (ICP, PerkinElmer Optima 5300DV, PerkinElmer,
USA, uncertainty < 2% for all investigated species) for the concentrations
of Na, Ca, Mg and P. Ionic chromatography (IC, Metrohm
741 Compact IC, Metrohm AG, Switzerland, uncertainty < 5%
for all investigated species) was used for measurement of the
SO 4 and PO 4 concentration. Conductivity measurement of the
outlet stream was used for the verification of an equilibrium
state in the column. pH measurements of the samples were performed
using an standard pH electrode (WTW pH/Cond 340i/SET,
(3)
Fig. 2. Relative fraction of phosphate species as a function of pH.
WTW Wissenschaftlich-Technische Werkstätten GmbH, Germany,
uncertainty after calibration ±0.01). The outlet temperature (TI-4
in Fig. 1) and the pressure at the pressure sensor (PI-1 in Fig. 1)
were used for the calculation of the density in the system. The feed
solution was prepared with deionized water and analytical grade
compounds (Boom B.V., The Netherlands).
4. Results and discussion
4.1. Experimental results phosphate salts
The solubility of Na 2 HPO 4 , NaH 2 PO 4 and CaHPO 4 was investigated
in a range of 20.5–24.2 MPa and 665–690 K. For the sodium
phosphates a feed concentration of 0.05 M was used; for CaHPO 4
a feed concentration of 0.05–0.5 mM was used. 2 Na 2 HPO 4 and
NaH 2 PO 4 showed occasional plugging, apparently independent of
temperature, pressure and length of the experiment. The plugging
in this case occurred at the filter in the outlet section, which could
be removed by rinsing with nitric acid (cf. Fig. 1). CaHPO 4 on the
other hand showed severe plugging in the preheater and the inlet
section. Although the preheater was switched off to avoid plugging
in later experiments with CaHPO 4 , plugging of the preheater
and the inlet section occurred before an equilibrium in the column
was achieved. Therefore, no further experiments on CaHPO 4
were performed. Since CaHPO 4 has a low solubility at ambient state
(∼200 mg L −1 [30]), a further decrease to minimal solubilities at elevated
temperatures was to be expected resulting in the observed
plugging. For all experiments with phosphate salts, the composition
of the samples was analyzed in regard of the content of Na + ,P
and PO 3−
4 . Each data point results from the experimental results of
four to six individual samples at one temperature and pressure.
Phosphates form a complex conjugated acid/base system of
the acid/base pairs of H 3 PO 4 ,H 2 PO − 4 , HPO2− 4 and PO 3−
4 (cf. Fig. 2),
wherein all forms act as weak acids/bases and as buffer (also see
Eq. (4)–(6)).
H 3 PO 4 + H 2 O ⇌ H 2 PO 4 − + H 3 O + (pK = 2.12) (4)
2 The feed concentration was decreased in order to avoid plugging.

4 I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8
Fig. 3. Solubility of sodium and phosphate (a) and phosphorus and phosphate (b) as function of density for the experiments on Na 2HPO 4; ○ corresponds to sodium
concentration; □ corresponds to phosphorus concentration; ▽ corresponds to phosphate concentration.
H 2 PO − 4 + H 2 O ⇌ HPO 2−
4 + H 3O + (pK = 7.21) (5)
HPO 2−
4 + H 2O ⇌ PO 3−
4 + H 3O + (pK = 12.63) (6)
By changes of the pH in the system, the equilibria and the relative
fractions of the different steps can be changed.
4.1.1. Disodium hydrogen phosphate
Fig. 3 shows the concentrations of the three analyzed compounds
(Na + , P and PO 3−
4 ) as a function of the molar density. Each
data point consists of five samples of one experimental run at
one set temperature and pressure. The pH value for these samples
were in the range of 6.5–7.5, while the pH of the 0.05 M feed
solution was calculated as 9.18 (calculated with OLI TM , a simulation
software for electrolyte chemistry). As can be seen, the concentration
of phosphorus (analyzed by ICP) and phosphate (analyzed by
IC) coincide within experimental errors. It can be concluded that
no decomposition of the phosphate happened. According to the
molar composition of Na 2 HPO 4 , a factor 2 between the concentration
of phosphate/phosphorus to sodium was to be expected
in the samples. Regarding the sodium concentration, one can see
that all measured concentrations (with one exception) were only
slightly above the corresponding phosphorus/phosphate concentration
and did not reach a ratio of 2. A possible explanation for
this could be a parallel hydrolysis like described in the following
equation:
Na 2 HPO 4 + H 2 O ⇌ NaOH ↓+NaH 2 PO 4 (7)
The hereby produced sodium hydroxide is assumed to have
a lower solubility than the other present compounds and to
precipitate at the experimental conditions. The effluent stream consequently
would leave the system at a lower sodium/phosphate
ratio than the influent stream. A continued reaction to phosphoric
acid can be excluded since the effluent pH was between 6.5 and
7.5. Resulting from this, only H 2 PO4 − and HPO4 2− are present in
the system (cf. Fig. 2). A correction of the cation concentration like
proposed in Eq. (9) does not lead a significant increase in the cation
concentration. It is assumed that the buffer capacity of the system
prevents a further decrease in pH. Thereby, a direct correlation of
the pH to the amount of precipitated NaOH cannot be derived. For
the further quantitative description of the solubility, the sodium
concentration is used in accordance to previous works. One has to
be aware that the actual solubility of Na 2 HPO 4 is underestimated
to a certain degree by this approach.
Fig. 4. Solubility of Na 2HPO 4 as a function of density; ○, this work; dashed line
represents the description of the experimental data with Eq. (3).
The sodium concentration for the experiments with Na 2 HPO 4
can be found in Fig. 4. Furthermore included in this graph is the
description of the experimental data with Eq. (3). As can be seen,
the approach is in good agreement with the experimental data.
More details on the approach and fitting procedure can be found in
Section 2 and in previous works [23,24].
The actual experimental data containing temperature, pressure,
pH and sodium concentration can be found in Table 2; the parameters
for Eq. (3) for Na 2 HPO 4 can be found in Table 1.
Table 1
Model parameters of the salts MgSO 4 ,Na 2HPO 4 and NaH 2PO 4 for Eq. (3).
Salt H/J·mol −1 S/J·mol −1 K −1 n
MgSO 4 −8257 −154.4 3.31
Na 2HPO 4 −142411 −351.4 5.37
NaH 2PO 4 −35582 −152.4 3.47
KH 2PO 4 −84569 −271.2 4.33

I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8 5
Table 2
Experimental results for Na 2HPO 4; refers to the standard deviations of the measured
quantities during the experiment.
T /K ± T p /MPa ± p m(Na + )/mmol kg −1 ± p pH ± pH
680.9 ± 0.0 23.21 ± 0.01 1.17 ± 0.31 7.31 ± 0.19
679.8 ± 0.1 21.97 ± 0.01 0.90 ± 0.21 7.29 ± 0.12
679.5 ± 0.1 21.03 ± 0.03 0.55 ± 0.24 7.41 ± 0.05
668.1 ± 0.4 22.99 ± 0.01 4.42 ± 0.18 7.16 ± 0.07
674.2 ± 0.2 22.93 ± 0.01 2.03 ± 0.24 6.53 ± 0.35
673.9 ± 0.1 21.94 ± 0.02 0.96 ± 0.18 7.11 ± 0.09
4.1.2. Sodium dihydrogen phosphate
Fig. 5 shows the concentrations of Na + and PO 3−
4 as a function
of the molar density. Each data point consists of five samples
of one experimental run at one set temperature and pressure.
The data for the phosphorus concentration coincides to a high
degree with the phosphate concentration and is therefore not
included in this figure. The pH value for these samples were in
the range of 2.7–3.2, while the pH of the 0.05 M feed solution was
calculated as 4.54 (calculated with OLI TM , a simulation software
for electrolyte chemistry). According to the molar composition
of NaH 2 PO 4 , the concentrations of phosphorus/phosphate and
sodium were expected to be equal. Yet, all sodium concentrations
were below the corresponding phosphorus/phosphate concentrations.
A hydrolysis reaction is assumed as the reason for this in
accordance with previous observations [25]. This hydrolysis leads
to a formation of NaOH, which precipitates. The parallel formed
HCl stays in solution and leaves the system with the effluent. This
leads to a decrease in pH as can be found for these experiments. A
correction of this hydrolysis reaction is possible with the following
approach:
m H3 O +
m total (Na)
= m −
H 2 PO = m
4
NaOH
= m analyzed (Na) + m Hydrolysis (Na)
(8)
= m analyzed (Na) + m(NaOH)
= m analyzed (Na) + 10 −pH
As can be seen from Fig. 5, the correction shows in this case a
good coincidence with the results for the phosphate/phosphorus
results. For further evaluation of the results, the corrected sodium
concentration is used.
The corrected sodium concentration for the experiments with
NaH 2 PO 4 can be found in Fig. 6. Furthermore included in this graph
is the description of the experimental data with Eq. (3). As can be
Fig. 6. Solubility of NaH 2PO 4 as a function of density; ○, this work; dashed line
represents the description of the experimental data with Eq. (3).
Table 3
Experimental results for NaH 2PO 4; refers to the standard deviations of the measured
quantities during the experiment.
T /K ± T p /MPa ± p m(Na + )/mmol kg −1 ± c pH ± pH
671.4 ± 0.1 23.08 ± 0.04 6.62 ± 0.84 2.75 ± 0.04
683.4 ± 0.6 23.20 ± 0.01 5.04 ± 0.38 3.05 ± 0.05
673.5 ± 0.1 21.17 ± 0.01 3.36 ± 0.30 2.86 ± 0.04
674.3 ± 0.1 20.27 ± 0.01 2.82 ± 0.12 3.16 ± 0.02
691.3 ± 0.2 24.20 ± 0.02 4.58 ± 0.44 3.00 ± 0.02
694.6 ± 0.0 20.50 ± 0.01 1.36 ± 0.03 3.05 ± 0.06
seen, the approach is in good agreement with the experimental
data. More details on the approach and fitting procedure can be
found in Section 2 and in previous works [23,24].
The actual experimental data containing temperature, pressure,
pH and corrected sodium concentration can be found in Table 3; the
parameters for Eq. (3) for Na 2 HPO 4 can be found in Table 1.
Fig. 5. Solubility of sodium and phosphate (a) and comparison between the corrected solubility of sodium and the solubility of phosphate (b) as function of density for the
experiments on NaH 2PO 4; ○ corresponds to sodium concentration; ▽ corresponds to phosphate concentration; △ corresponds to corrected sodium concentration.

6 I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8
Fig. 7. Comparison of the solubilities of Na 2HPO 4, NaH 2PO 4 (this work) and KH 2PO 4
[26] as function of density; dashed line corresponds to Na 2HPO 4; solid line corresponds
to NaH 2PO 4; dashed-dotted line corresponds to KH 2PO 4.
4.1.3. Comparison phosphate salts
Fig. 7 shows a comparison of the results for the phosphate salts
Na 2 HPO 4 and NaH 2 PO 4 presented in this work and the results for
KH 2 PO 4 by Wofford et al. [26]. The comparison shows that the solubility
of potassium phosphate in supercritical water is lower than
the solubility for sodium phosphates. This agrees with the assumption
that the molecule size or in this case the cation size is related
to the solubility as presented in previous works [24,31]. In these
works, a direct relation between the cation of the investigated chloride
salts and the actual solubility was found (Li > Na > K). As ions
are present in supercritical water only to a small amount, the majority
of the non-water species present is associated as molecules and
complexes. To keep these molecules in solution, hydration has to
occur. This hydration is due to the decreased amount and strength
of hydrogen bondings in supercritical water less present than at
ambient state. Therefore, a hydration of larger molecules is more
difficult as more hydrogen bondings have to be established over a
larger distance [24].
Upon a comparison between the solubilities of KH 2 PO 4 and the
two sodium phosphates, it can be seen that the solubility of KH 2 PO 4
is lower in agreement with the findings for the alkali chlorides and
nitrates. As one compares the solubilities of the phosphates investigated
in this work, NaH 2 PO 4 has a slightly higher solubility than
Na 2 HPO 4 in the investigated density range. It can be concluded here
as well that the molecule size is of influence since Na 2 HPO 4 and
the resulting hydration sphere is larger by a small amount than
NaH 2 PO 4 and thereby resulting in the lower solubility.
4.2. Experimental results sulfate salts
Two sulfate salts that are commonly found in water streams,
MgSO 4 and CaSO 4 , were investigated in the range of 18.8–23.2 MPa
and 655–675 K. CaSO 4 has a low solubility product at ambient conditions
(K sp = 4.93 × 10 −5 [30]) while the solubility of MgSO 4 is
comparably high (K sp = 4.67 [30]). Therefore, a low feed concentration
(1 mM and below) was used to avoid plugging. Despite this
low feed concentration, plugging occurred in and just before the
preheater for both salts. The tubing in the preheater has a diameter
of 1.588 mm and thereby only a small cross section. A further
Fig. 8. Solubility of MgSO 4 as a function of density; ○, this work; dashed line represents
the description of the experimental data with Eq. (3).
reduction in concentration did not solve this issue and just postponed
the point of plugging by several minutes to hours. To solve
this problem, the preheater was turned off in order to avoid precipitation
before the solution enters the oven. This was successful
for MgSO 4 , yet not for CaSO 4 . Due to thermal conductance, parts
of the preheater and parts just after the preheater were heated up
apparently far enough to precipitate parts of the feed solution in
case of CaSO 4 . This indicates a higher solubility of MgSO 4 at supercritical
pressures and slightly elevated temperatures in comparison
to CaSO 4 similar to the behavior of CaHPO 4 (cf. previous section).
Therefore, only results for the measurements of MgSO 4 can be presented
here. Attempts to remove the plugging via ultrasound and
rinsing with concentrated nitric acid/Piranha solution (3:1 conc.
H 2 SO 4 to 30 % H 2 O 2 ) did not succeed for both salts.
4.2.1. Magnesium sulfate
The experimental data for the measurements of MgSO 4 can be
found in Fig. 8. The overall solubilities are low and in the range
of 10 −4 to 10 −5 mol kg −1 . Thereby, the concentrations were in the
lower detection range of the analytical methods applied here. Furthermore
included in this graph is the quantitative description of
the experimental data via Eq. (3). As can be seen, the approach is
in good agreement with the experimental data. For all samples,
a pH value of between 3.9 and 4.6 was measured, while the feed
solution of 1 mM MgSO 4 a pH value of 6.98 was determined (calculated
with OLI TM , a simulation software for electrolyte chemistry).
This decrease in pH indicates the occurrence of a parallel hydrolysis
reaction [25]. Nevertheless, a correction of the cation concentration
for a parallel hydrolysis reaction as done for MgCl 2 and CaCl 2
was not performed due to the following. The values for the cation
and anion concentration coincide and the deviation between the
anion and cation concentration was within the experimental error
(cf. Fig. 9). Therefore, no excess amount of one of the species magnesium
or sulfate was present in the sample which would make
a correction necessary. If one performs a correction of the cation
concentration for the hydrolysis as proposed in Leusbrock et al.
[25] (also see Eq. (9)), a difference of up to 80% between the anion
and the cation concentration (cf. Fig. 9) would be the result. This
was not considered as a reasonable approach for the evaluation of
the experimental results. Still, one has to be aware that hydrolysis

I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8 7
Fig. 9. Solubility of magnesium and sulfate (a) and comparison of sulfate concentration and possible correction (b) as function of density for the experiments of MgSO 4 ; ○
corresponds to sulfate concentration; △ corresponds to magnesium concentration; □ corresponds to corrected magnesium concentration.
Table 4
Experimental results for MgSO 4 ; refers to the standard deviations of the measured
quantities during the experiment.
T /K ± T/K p /MPa ± p/MPa m(Mg 2+ )/10 −5 mol kg −1 pH
674.5 ± 0.6 23.28 ± 0.55 4.24 4.55
674.3 ± 0.5 23.28 ± 0.54 3.13 4.53
674.5 ± 0.6 22.71 ± 0.56 2.35 4.33
659.8 ± 0.5 22.96 ± 0.54 5.73 4.31
659.5 ± 0.6 22.96 ± 0.56 5.03 4.28
658.9 ± 0.6 22.96 ± 0.56 6.92 4.23
672.0 ± 0.6 22.40 ± 0.60 1.64 4.18
671.9 ± 0.6 21.67 ± 0.60 1.87 4.23
672.0 ± 0.6 21.69 ± 0.60 1.65 4.24
672.4 ± 0.6 21.12 ± 0.63 1.76 4.25
672.5 ± 0.6 21.12 ± 0.61 1.66 4.22
654.8 ± 0.5 23.10 ± 0.50 11.41 4.24
654.3 ± 0.6 23.08 ± 0.57 10.38 4.02
654.1 ± 0.6 18.80 ± 0.56 1.46 3.92
654.4 ± 0.6 18.81 ± 0.55 1.21 4.04
occurs as indicated by the pH decrease.
m H3 O + = 2 · m H 2 SO 4
= 2 · m Mg(OH)2
m total (Mg) = m analyzed (Mg) + m Hydrolysis (Mg)
(9)
= m analyzed (Mg) + m(Mg(OH) 2 )
= m analyzed (Mg) + 0.5 · m(H 2 SO 4 )
= m analyzed (Mg) + 0.5 · 10 −pH
The actual experimental data containing temperature, pressure,
pH and magnesium concentration can be found in Table 4; the
parameters for Eq. (3) for MgSO 4 can be found in Table 1. In contrast
to the results on the phosphate salts, each data point represents one
sample. Thereby, the accuracy of the measurement is lower.
5. Conclusions
In the course of this work, the solubilities of the sulfate salts
MgSO 4 and CaSO 4 in a range of 18.8–23.2 MPa and 655–675 K as
well as of the phosphate salts Na 2 HPO 4 , NaH 2 PO 4 and CaHPO 4
in a range of 20.5–24.2 MPa and 665–690 K were investigated. It
has been found that experiments with CaSO 4 and CaHPO 4 lead to
plugging of the equipment with the current configuration of the
setup due to low solubilities even at a subcritical state. Therefore,
no solubility data can be presented at this point for these salts.
For the other salts, experiments have been conducted successfully.
Here, deviations between the anion and cation concentrations
occurred due to a parallel hydrolysis reaction. These could partly
be corrected by inclusion of the measured pH values. The extent of
the hydrolysis depends on the temperature and pressure during the
experiments and the investigated compound as found in previous
articles of the authors [24,25]. The results of the experiments were
correlated with a semi-empirical model. This correlation showed a
good coincidence between experiments and proposed model.
For a better understanding of the behavior of phosphate salts in
supercritical water, more experiments with further salts and different
conditions have to be conducted due to the complexity (pH
dependency, equilibria between different stages) of the phosphate
system.
Acknowledgements
The authors would like to thank the analytical team of Wetsus
for their contribution in the analysis of the samples.
This work was performed in the TTIW-cooperation framework
of Wetsus, centre of excellence for sustainable water technology
(www.wetsus.nl). Wetsus is funded by the Dutch Ministry of Economic
Affairs, the European Union Regional Development Fund, the
Province of Fryslân, the City of Leeuwarden, and the EZ/Kompas
program of the ‘Samenwerkingsverband Noord-Nederland’. The
authors like to thank the participants of the research theme Salt
for their financial support.
References
[1] S. Stucki, F. Vogel, C. Ludwig, A.G. Haiduc, M. Brandenberger, Catalytic gasification
of algae in supercritical water for biofuel production and carbon capture,
Energy & Environmental Science 2 (5) (2009) 535–541.
[2] G. Brunner, Near critical and supercritical water. Part I. Hydrolytic and
hydrothermal processes, The Journal of Supercritical Fluids 47 (3) (2009) 373.
[3] T.J. Park, J.S. Lim, Y.W. Lee, S.H. Kim, Catalytic supercritical water oxidation
of wastewater from terephthalic acid manufacturing process, The Journal of
Supercritical Fluids 26 (3) (2003) 201–213.
[4] M.D. Bermejo, M.J. Cocero, Supercritical water oxidation: a technical review,
AIChE Journal 52 (11) (2006) 3933–3951.
[5] E. Lester, P. Blood, J. Denyer, D. Giddings, B. Azzopardi, M. Poliakoff, Reaction
engineering: the supercritical water hydrothermal synthesis of nano-particles,
The Journal of Supercritical Fluids 37 (2) (2006) 209.
[6] Y. Hakuta, H. Ura, H. Hayashi, K. Arai, Effects of hydrothermal synthetic conditions
on the particle size of -AlO(OH) in sub- and supercritical water using a
flow reaction system, Materials Chemistry and Physics 93 (2–3) (2005) 466.

8 I. Leusbrock et al. / J. of Supercritical Fluids 54 (2010) 1–8
[7] A. Kruse, E. Dinjus, Hot compressed water as reaction medium and reactant:
properties and synthesis reactions, The Journal of Supercritical Fluids 39 (3)
(2007) 362.
[8] P.E. Savage, A perspective on catalysis in sub- and supercritical water, The
Journal of Supercritical Fluids 47 (3) (2009) 407.
[9] D.E. Knox, Solubilities in supercritical fluids, Pure Applied Chemistry 77 (2005)
513–530.
[10] T. Clifford, Fundamentals of Supercritical Fluids, Oxford University Press, 1999.
[11] F.J. Armellini, J.W. Tester, G.T. Hong, Precipitation of sodium chloride and
sodium sulfate in water from sub- to supercritical conditions: 150–550 ◦ C,
100–300 bar, The Journal of Supercritical Fluids 7 (3) (1994) 147.
[12] M. Hodes, P. Griffith, K.A. Smith, W.S. Hurst, W.J. Bowers, K. Sako, Salt solubility
and deposition in high temperature and pressure aqueous solutions, American
Institute of Chemical Engineers Journal 50 (2004) 2038–2049.
[13] M. Hodes, P.A. Marrone, G.T. Hong, K.A. Smith, J.W. Tester, Salt precipitation
and scale control in supercritical water oxidation. Part A. Fundamentals and
research, The Journal of Supercritical Fluids 29 (3) (2004) 265.
[14] P.A. Marrone, M. Hodes, K.A. Smith, J.W. Tester, Salt precipitation and scale control
in supercritical water oxidation. Part B. Commercial/full-scale applications,
The Journal of Supercritical Fluids 29 (3) (2004) 289.
[15] A. Kruse, Hydrothermal biomass gasification, The Journal of Supercritical Fluids
47 (3) (2009) 391–399.
[16] P.A. Marrone, G.T. Hong, Corrosion control methods in supercritical water oxidation
and gasification processes, The Journal of Supercritical Fluids 51 (2)
(2009) 83–103.
[17] G. Brunner, Near and supercritical water. Part II. Oxidative processes, The Journal
of Supercritical Fluids 47 (3) (2009) 382.
[18] M. Schubert, J.W. Regler, F. Vogel, Continuous salt precipitation and separation
from supercritical water. Part 1: Type 1 salts, The Journal of Supercritical Fluids
52 (1) (2010) 99–112.
[19] K. Prikopsky, B. Wellig, P.R. von Rohr, SCWO of salt containing artificial wastewater
using a transpiring-wall reactor: experimental results, The Journal of
Supercritical Fluids 40 (2) (2007) 246.
[20] B. Kruse, D. Forchheim, F. Ottinger, J. Zimmermann, Alkali salts in hydrothermal
biomass gasification: chance and challenge, in: Proceedings of the 9th
International Symposium on Supercritical Fluids, 2009.
[21] M. Schubert, J.W. Regler, F. Vogel, Continuous salt precipitation and separation
from supercritical water., Part 2. Type 2 salts and mixtures of two salts, The
Journal of Supercritical Fluids 52 (1) (2010) 113–124.
[22] G. Tchobanoglous, F.L. Burton, H.D. Stensel, Wastewater Engineering: Treatment
and Reuse, McGraw-Hill Science Engineering, 2003.
[23] I. Leusbrock, S. Metz, G. Rexwinkel, G.F. Versteeg, Quantitative approaches
for the description of solubilities of inorganic compounds in near-critical
and supercritical water, The Journal of Supercritical Fluids 47 (2) (2008)
117–127.
[24] I. Leusbrock, S.J. Metz, G. Rexwinkel, G.F. Versteeg, Solubility of 1:1 alkali
nitrates and chlorides in near-critical and supercritical water, Journal of Chemical
and Engineering Data 54 (12) (2009) 3215–3223.
[25] I. Leusbrock, S.J. Metz, G. Rexwinkel, G.F. Versteeg, The solubility of magnesium
chloride and calcium chloride in near-critical and supercritical water,
The Journal of Supercritical Fluids, in press, 10.1016/j.supflu.2009.12.015.
[26] W.T. Wofford, P.C. Dellorco, E.F. Gloyna, Solubility of potassium hydroxide and
potassium phosphate in supercritical water, Journal of Chemical and Engineering
Data 40 (4) (1995) 968–973.
[27] J. Chrastil, Solubility of solids and liquids in supercritical gases, Journal of Physical
Chemistry 86 (15) (1982) 3016–3021.
[28] R.E. Mesmer, W.L. Marshall, D.A. Palmer, J.M. Simonson, H.F. Holmes, Thermodynamics
of aqueous association and ionization reactions at high-temperatures
and pressures, Journal of Solution Chemistry 17 (8) (1988) 699–718.
[29] W. Wagner, The IAPWS formulation 1995 for the thermodynamic properties of
ordinary water substance for general and scientific use, Journal of Physical and
Chemical Reference Data 31 (2) (1999) 387.
[30] D.R. Ride, CRC Handbook of Chemistry and Physics, CRC Press, 2004.
[31] P. Dell’Orco, H. Eaton, T. Reynolds, S. Buelow, The solubility of 1:1 nitrate electrolytes
in supercritical water, The Journal of Supercritical Fluids 8 (3) (1995)
217.