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3. June 2019
Master Project
In situ measurement of ammonium
in marine watersSøren Læsaa
AU � Engineering
Datasheet
Title In situ measurement of ammonium in marine waters
Subtitle Master Project, 30 ECTS
Author Søren Læsaa, 201602395
Institution Department of Engineering, Aarhus University
Arctic Research Center, Aarhus University
Supervisors Lise Lotte Sørensen
Arctic Research Centre, Aarhus University
Jesper Nørlem Kamp
Department of Engineering, Aarhus University
Anders Feilberg
Department of Engineering, Aarhus University
Submitted 03-06-2019
Front page photo https://wallimpex.com/data/out/315/under-water-
backgrounds-6928122.jpg
Number of pages 43
2
AU � Engineering
Abstract
The challenges on measuring NHx (Total ammonia nitrogen) in seawater with the OPA method
has been investigated. It was found that magnesium and calcium precipitant increased the
turbidity of the sample to a point where �uorescence detection was no longer possible.
To counteract this precipitation the e�ect of membrane separation were researched. The iso-
lating of ammonium form seawater was tested with four sintered PTFE membranes. The best
performing membrane was BM100 with a selectivity of 4.01. In the set-up used here, up to 90
% of the NHx were recovered while 85 % of the salt was restrained by using an HCl solution to
drag NHx across the membrane. However, the membrane separation procedure was discarded
as it slowed the signal response considerably.
The other approach tested was the use of citrate as a chelating agent. The addition of 200 mM
of citrate proved capable of preventing precipitation. This, mechanically simpler, sensor set-up
reacted 14 times faster on NHx changes than the membrane sensor.
An online sensor was constructed by the chelating agent principle. Calibration showed a range
from 60 nM to 3.5 �M with an uncertainty of 10 nM. The sensor was tested at Kattegatcentret
in Grenaa Denmark for eight days. Despite NHx concentrations close to the lower detection
limit did the sensor show good performance.
The signal interference from amines was tested with methylamines. Trimethylamine sowed no
sign of reaction. Dimethylamine was found to react with OPA but without any �uorescence
interference. The methylamine product showed some �uorescence yield at 425 nm with an
intensity of 0.035 % compared to the ammonia product. Comparing the methylamine and
ammonia �uorescence spectra showed a methylamine peak at 520 nm there did not show for
ammonia. This indicates that methylamine can be detected with the OPA method at 520 nm,
however, this is mostly theoretical as the signal intensity is very week.
3
AU � Engineering Contents
Contents
1 Introduction 5
2 Theory 72.1 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Freshwater OPA method 113.1 Seawater sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Membrane 134.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.4 Membrane transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.5 Membrane selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.6 Sensor response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Chelating agents 205.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2 Materials and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.3 Initial test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.4 Bu�er solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.5 Citrate concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.6 Sensor response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 Seawater OPA method 256.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256.2 pH e�ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7 Amines 28
8 Monitoring test 30
9 Discussion 31
10 Conclusion 33
A Derivation of carbonate precipitation equation 37
B Statistics 39B.1 Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B.2 Cin�dance interval for membrane transport . . . . . . . . . . . . . . . . . . . 39B.3 Con�dance interval for membrane selectivity . . . . . . . . . . . . . . . . . . . 40
C Simulink model of the membrane sensor 41
D Membrane properties 42
E Reagent cost 43
4
AU � Engineering Introduction
1 Introduction
The interest in NHx (Total ammonia nitrogen) detection in seawater originates from its impor-
tance for the ecological cycle. The seawater NHx originates from the degradation of organic
matter or nitrogen �xation form the water surface and serves as a nutrition source for phyto-
plankton [1]. The desire to map NHx occurrences in the oceans has been intensi�ed in recent
years alongside climate awareness. This is due to the indications that airborne ammonia can
cause particle nucleation that a�ects the climate and increase air pollution. In this contexts,
it is relevant to investigate the exchange of ammonia between ocean and atmosphere including
the NHx concentration in the ocean [2, 3].
Since the task of measuring NHx is neither new nor trivial, various methods have been proposed
for this over time. The OPA (Ortho-PhthalAldehyde) method was originally designed for detect-
ing amino acids by Marc Roth [4] in 1971. In 1989 the selectivity for ammonia was optimized by
Z. Genfa and P. K. Dasgupta [5] who changed the supporting reagent from mercaptoethanol to
sul�te. This project is based on the optimized OPA method as it has shown the best sensitivity
for ammonia and less toxicity than other methods [6].
The backbone of the OPA method for ammonia is the reaction between OPA, sul�te, and
ammonia to form the �uorescence compound 2H-Isoindole-1-sulfonate. The concentration of
ammonia can thereby be detected indirectly by measuring the �uorescence intensity of the sam-
ple [5, 7].
The general principle of measuring ammonium by this method seems fairly simple but the na-
ture of seawater composition has resulted in a variety of procedures [8]. A general challenge in
the ocean environment is the presence of di�erent trace elements that might precipitate with
the reactants. Furthermore, the sample is measured at high alkalinity to ensure complete NHx
detection by converting ammonium to ammonia. This shift in pH can also disturb the solubil-
ity equilibria of divalent ions in the sample [9�11]. The issue with these potential sources of
precipitation is that it can compromise the �uorometric detection by changing the turbidity of
the sample. All of the studies found uses chelating agents or measure at less than ideal pH to
accommodate for this possible error. The purpose of chelating agents is to bind divalent ions
to hinder the formation of precipitating salts.
This project will approach the precipitation problem from a di�erent angle. Namely by adding a
membrane separation to the set-up with the goal of isolating ammonia from the troublesome sea
salts. This process should limit the e�ect of variations in trace element concentrations as the
salt would not be in direct contact with the reagents. In addition, the chelating agent method
will be tested. This is done to evaluate the robustness of the reported procedures and to serve
as a baseline in comparison to the membrane set-up.
The practical working procedure for the method range from purely manual to automated sample
detection [8, 12�14]. Common to them all is that sampling is still done manually. An overview
of NHx measuring cruises show that the complete manual method is preferred and that the
expected range of NHx in seawater lies between 15 nM to 32 �M [2]. The issue with sample
collection is that human contact comes with a risk of contamination and that the labor-intensive
method leads to an under-sampling of sea measurements compared to air monitoring.
The contamination risk for NHx originates from multiple sources. As both human breath and
sweat contain NHx exceeding the expected seawater concentrations is manual sampling and
measuring associated with high risk of contamination. A breath containing 0.5 ppm ammonia
5
AU � Engineering Introduction
[15] equilibrates to an liquid concentration of 0.1 mM NHx at 20 �C [16] and mean sweat con-
centration lies around 2.3 mM NHx [17]. Besides the human contamination risk is the seawater
NHx in constant equilibrium with its surroundings, this implies both biological activity in the
seawater and exchange with the atmosphere. The act of capturing a sample disturb these equi-
libriums meaning that biological activity in the sample will change the NHx content over time.
Changes in temperature and ammonia air concentration will alter the solubility of ammonia in
the sample and introduce an air to sample interaction physically changing the sample concen-
tration. [16].
To minimize the uncertainties above and the manual workload this project will aim at establish-
ing a completely online measurement set-up. An automated sampling eliminates the need for
humane contact and makes it possible to measure the ammonia concentration almost directly
in the environment minimizing equilibrium changes.
Another bene�t of an online system is the possibility to use it as a regulation sensor for instance
in �sh farming. Ammonia is toxic to marine life in high concentrations [18] and the dense
population within a �sh farm can cause the NHx level to rice well above natural concentrations
[19]. In this contexts can an online sensor both be used as an environmental control of �sh
farming pollutant but also as a tool for the farmers to react on critical rise in the ammonium
concentration before loss in �sh stock.
Even though the OPA method is considered highly selective, there is reported interference from
amines among other compounds [11, 13, 20]. The interference seems to be caused by molecules
there can react with OPA in a similar fashion as ammonium. The �uorescence yield of these
reactions are generally low and therefore causing little e�ect on the NHx detection. However, if
the �uorescence spectra of for instance amines is generally di�erent from the ammonia spectra
it should be possible to detect both compounds in the same sample. This is done by measuring
the �uorescence intensity at multiple wavelengths of light.
The interest in amines emerges from its ability to produce atmospheric aerosols which are a
threat to both the climate and public health [21]. Even though the estimated amine concen-
tration in oceanic waters lies around 50 nM [22] is the amine e�ect on particle initiation still
relevant, as the particle formation rate for amines is magnitudes higher than for ammonia [23].
The amine interference of the derived method will be tested with methylamines. The �uores-
cence spectra of the amine products will also be investigated for a shift in peak intensity that
could lead to a combined NHx and amine sensor based on the OPA method.
6
AU � Engineering Theory
2 Theory
2.1 Chemistry
The overall reaction scheme between OPA, sul�te, and ammonia are shown in �gure 1. Al-
though the exact mechanism is unknown, is the reaction considered to be quite selective towards
ammonia when performed in a alkaline environment [7]. The reaction is generally considered
irreversible. The �uorescence signal is, however, reported to decrease after a stable period
[12, 13]. This indicates that some sort of degradation of 2H-Isoindole-1-sulfonate occurs. At
room temperatur, the �uorescence signal peaks after 3 to 4 hours and slowly starting to decrease
after 10 to 20 hours [12]. The reaction speed can be increased by raising the temperature. Most
automated samplers run at 70 to 85 �C with a reaction time of a couple of minutes [8]. Higher
temperature also increases the degradation of 2H-Isoindole-1-sulfonate. The use of automated
set-up ensures an even reaction time and conditions between samples, meaning that the time
and temperature dependent errors is minimised in such an con�guration.
Figure 1: The reaction between OPA, sulphite, and ammonia to form 2H-Isoindole-1-sulfonate [7, 24]
There is, as mentioned not found any studies on the complete mechanism, but two papers were
found to investigate the reactions of OPA and ammonia alone. T. DoMinh et al.[25] worked
on OPA reactions with ammonia and amines in 1976. They found that both ammonia and
primary amines could react with OPA to form isoindole based structures. Secondary amines
would also react with OPA but formed a benzofuran based structure. Both of the products are
shown in �gure 2. An paper from 2008 by E. Kulla and P. Zuman [26] investigates the OPA
and ammonium reaction further. They revealed more than 15 intermediate and �nal reaction
products and reported that the pH should exceed 9.3 to close the nitrogen ring in the isoindole
based structures.
Figure 2: Potential products formed from OPA. Ammonia and primary amine on the left and secondary
amine to the right. [25]
7
AU � Engineering Theory
2.2 Fluorescence
Fluorescence detection is a variety of the general light detecting methods. Fluorescence detec-
tion exploits that some compounds can maintain an excited state for a while before collapsing to
the natural state and thereby emitting a photon. This delay in emission allows for the excitation
light source to be switched o� and the emitted photon is detected against a dark background,
as the only light source is the �uorescence molecules. This minimize scatter and re�ecting noise
from the excitation light source.
The �uorescence detection can be optimized by examining the �uorescence spectra of the de-
sired compound. A excitation and emission spectra of 2H-Isoindole-1-sulfonate are shown in
�gure 3. The detection is speci�ed for 2H-Isoindole-1-sulfonate by ensuring that the excitation
source is focused around 362 nm and �ltering the emission light so only light at 423 nm passes
through to the detector.
Figure 3: Excitation and emission spectra of reaction product of OPA-sul�te-ammonia.[11]
The �uorescent characteristics of a compound is di�cult to predict as there are multiple com-
positions that can create opportunities for a �uorescent state. One of these conditions is the
presence of conjugated �-electrons. In the case of 2H-Isoindole-1-sulfonate, it seems likely that
the two conjugated rings are the source of the �uorescence [27]. This would imply that the
nitrogen lone pair contributes to the �uorescence characteristics of the molecule because of the
donor ability of the nitrogen atom.
Primary amines can react as well as ammonia with OPA to create similar structures [25] and the
additional carbon bond would change the donor ability for the nitrogen atom. This indicates that
an OPA-sul�te-amine product should have a di�erent �uorescence spectrum than 2H-Isoindole-
1-sulfonate. How a given amine would alter the spectra is hard to predict, e.g. if the peak is
shifted or alternative peaks are introduced it should be possible to measure amine concentration
with the OPA method by optimizing the �uorescence detection around its �uorescence nature.
8
AU � Engineering Theory
2.3 Precipitation
Previous studies have shown that a white solid precipitate in seawater as the pH increases
[28]. J. N. Plant et al. [29] reports this phenomenon to be caused by magnesium and calcium
hydroxides whereas B. Horstkotte et al. [20] claim it to be magnesium and calcium carbonate.
L. Irving [9] has shown that it is possible for both hydroxides and carbonates to precipitate in
seawater.
A theoretical precipitation point on the pH scale can be calculated by combining the solubility
of the salts with the pH dependency of the anions. As the hydroxide concentration is embedded
in the pH scale the precipitation point can be described by the following equations.
Ksp = [M2+] � [OH�]2 pH = 14� log([OH�])
pH = 14� log
√√√√ Ksp
[M2+]
(1)
The in�uence of pH on the carbonate concentration is more complex. Due to the divalent
acidity of carbonate is the concentration determined by two bu�er equilibriums.
10�pH
10�pKa;1=
[H2CO3]
[HCO�
3 ]
10�pH
10�pKa;2=
[HCO�
3 ]
[CO2�3 ]
The pH equation is derived and shown in appendix A and the equation for the pH at the
precipitation point are shown in equation 2 below.
pH = � log
√√√√√√ Ksp
[M2+]
[CO3;tot ]� 1 +
4 � 10�pKa;1
10�pKa;2� 2
p10�pKa;1p10�pKa;2
p10�pKa;2 � 10�pKa;1
(2)
The precipitation pH seen in table 1 is calculated as a pure solution and with �xed ion concentra-
tions. This is of cause not the case in natural waters thus conclusions must be drawn carefully.
The numbers indicate that seawater is generally supersaturated with calcium carbonate. Which
is also reported by L. Irving [9]. Considering that precipitation of calcium hydroxide requires
almost double the pH than calcium carbonate, the latter is properly the major contributor to
calcium precipitant. The precipitation pH for the magnesium salts is almost identical at the
used carbonate concentration. Considering that calcium has a strong a�nity for carbonates it
is possible that the carbonate supply is depleted forcing magnesium to precipitate as hydroxide.
In reality, this scenario and the general precipitation is strongly a�ected by the initial carbonate
concentration of the sample, thus both magnesium hydroxide and carbonate could be found in
the precipitant.
Hydroxides Carbonates
mol/l Ksp pH Ksp pH
Mg2+ 0.057 5:6 � 10�12 19.00 6:8 � 10�6 8.97
Ca2+ 0.011 4:7 � 10�61 12.31 4:9 � 10�9 6.69
Table 1: Precipitation pH calculated for seawater at 298 K. Seawater ion concentrations for 'Typical
Seawater' reported by Lenntech [30] were used. Solubility constants and acid dissociation
constants were given in C. E. Housecroft [27].
9
AU � Engineering Theory
In regard to the aim of avoiding precipitation, the opposite question might be of equal value:
how much of the magnesium and calcium should be removed in order to maintain a stable
solution at pH 11. This was calculated by rearranging the solubility equations to the form seen
in equation 3 to estimate the solubility point as the concentration of divalent cations.
[M2+] =Ksp
[OH�]2[M2+] =
Ksp
[CO2�3 ]
(3)
The hydroxide concentration at pH 11 is �xed to 0.001 M by the pH scale. The carbonate
concentration is a more �uctuating value. Using the �rst sets of equations in Appendix A it is
found that 82 % of the carbonate will be completely deprotonated at pH 11. Matched with the
carbonate concentration given for 'Typical Seawater' by Lenntech [30] the CO2�3 concentration
is calculated to be 0.0019 M.
The calculated solubility concentrations from equation 3, CS, can then be compared to the
estimated seawater concentrations for 'Typical Seawater' by Lenntech, CL, to estimate the
needed removal of cations to remain below insoluble concentrations.
CL � CS
CL
� 100 = Removal % (4)
Table 2 show the allowed Mg2+ and Ca2+ concentrations if precipitations should be avoided
and the removal e�ciencies necessary to meet these concentrations. Magnesium hydroxide
sets the aim with the highest removal needed. Considering a membrane �ltration both cations
and carbonates would be removed whereas the hydroxide concentration is given by the method.
Again pointing at the magnesium concentration as the most troublesome.
Hydroxides Carbonates
mol/l Solubility Removal % Solubility Removal %
Mg2+ 0.057 5:6 � 10�9 99.99997 3:6 � 10�3 81.05
Ca2+ 0.011 4:7 � 10�31 -26 2:6 � 10�6 99.93
Table 2: Solubility concentrations for Mg2+ and Ca2+ at 298 K and pH 11 calculated with the seawater
ion concentrations for 'Typical Seawater' reported by Lenntech [30]. The removal % show
is calculated between the solubility concentration and the ion concentration given for 'Typical
Seawater' when the dilution of reagents is taken into account. Solubility constants and acid
dissociation constants were given in C. E. Housecroft [27].
10
AU � Engineering Freshwater OPA method
3 Freshwater OPA method
An automated sensor con�guration was accomplished in previous work [28]. An overview of the
sensor is seen in �gure 4. This system is not compatible with salt water samples but is used as
a baseline for optimization.
Figure 4: Initial OPA sensor con�guration.
The OPA reagent utilized by the system was produced by dissolving 1.34 g of OPA in 200 ml
of 96 % ethanol whereafter the solution is diluted to 1 L with Milli-Q water.
The sul�te reagent is based on a phosphate bu�er. To prepare 1 L of phosphate bu�er 13.40
g of disodium phosphate were dissolved in 900 ml of Milli-Q water. 1 ml of formaldehyde was
added to the solution before the pH was adjusted to 11 by addition of 2 M sodium hydroxide
and Milli-Q water was added to reach a �nal volume of 1 L. Additional Milli-Q were added to
reach the �nal volume. The sul�te reagent was produced by dissolving 0.378 g of sodium sul�te
in 1 L of phosphate bu�er.
In this project the reagents and sample were supplied to the mixing tap at a rate of 0.36 ml/min
by an Ole Dich peristaltic pump. The combined solution was heated to 75 �C by a Supertherm
thermostat from Mikrolab Aarhus before the �uorescence was measured by a Perkin-Elmer LS-2
�lter �uorimeter.
Figure 5: Calibration of the OPA method with 95% con�dence interval
The set-up was calibrated with NHx standards from the Department of Environmental Science.
The calibration is depicted in �gure 5. Standards of 0, 0.71, 1.43, 2.86, 5.71, 10.00 and 19.99
�M NHx were supplied as the slope of the calibration were unknown. The Perkin-Elmer LS-2
11
AU � Engineering Freshwater OPA method
�lter �uorimeter is limited to 1 V detection signal equivalent to 3.7 �M NHx. New standards
were not obtained due to the complicated production and transport circumstances. An example
of the 95% con�dence interval calculation is given in Appendix B.1.
3.1 Seawater sample
The initial challenges that arise when seawater samples are to be analyzed by the method outlined
above are precipitation. This is demonstrated in �gure 6. The precipitation occurs when the
pH is adjusted to 11 for optimal �uorescence measurements. L. Irving [9] predicts that around
40 % of Magnesium and 30 % of calcium would be precipitated as hydroxides from a seawater
sample adjusted to pH 11 by sodium hydroxide. Other precipitates can of course occur as well
as reactions with the applied reagents. The main issue with the precipitation is inhibition of
the �uorescence detection. This inhibition is caused by the shadowing e�ect of the precipitated
particles, shadowing the �uorescence molecules from the excitation light so they do not �uoresce
or block the �uorescence light from reaching the photon sensor. Either way is the signal reduced
when the turbidity increases.
(a) Freshwater (b) Seawater
Figure 6: Sample clearness of freshwater and seawater prepered by the freshwater OPA method
12
AU � Engineering Membrane
4 Membrane
The idea behind the membrane approach is to purify the seawater sample in order to produce a
solution that is compatible with the freshwater OPA method. This is done by the addition of a
membrane separation before the sample inlet on the original method.
4.1 Theory
The function of a membrane is generally to separate two non-equilibrium systems with the
purpose of controlling the interaction between them. Thus, the driving forces of the membrane
transport are pushed by the di�erences in the systems separated by the membrane e.g. pressure,
heat or chemical potential gradients. For every gradient or driving force in the system, there
will be a corresponding �ux, respectively volume of solvent, heat or chemical concerning the
examples given before. Even though each gradient corresponds to a �ux, the single �uxes are
more or less in�uenced by every gradient in the system. For instance, can an electrical potential
di�erence drag ions across the membrane even though the chemical gradient is in equilibrium.
Furthermore is ion transport often carried by assisting water molecules creating a volume �ux
and a�ecting the pressure gradient. This interaction between the gradients and �uxes leads to a
n by n matrix system known as the phenomenological transport equations. This is an empirical
system of �ux terms where the number of exuations, and terms in each equation, is given by
number of posible gradients in the system. [31, 32]
Due to the mechanical simplicity of the sensor pressure, heat and current gradients are left out
of consideration, though these theoretically could have been used to enhance the ammonia �ux.
The system is restrained to pure chemical gradients. Due to the complexity of seawater, the
complete phenomenological transport equations are not trivial as each chemical species represent
a �ux and gradient. Equation 5 outlines the initial phenomenological transport equations for
seawater. Where Ji : Flux of species i . Li j : Phenomenological transport coe�cient. �Cj :
Chemical gradient of species j . �x : Membrane thickness. The phenomenological transport
coe�cient is an empirically de�ned number and is categorized into direct coe�cients, e.g. the
e�ect of ammonia gradient on the ammonia �ux, found in the matrix diagonal and coupling
coe�cients, e.g. the e�ect from other species gradient on the ammonia �ux, found outside the
matrix diagonal.
JNH3= LNH3NH3
�CNH3
�x+ LNH3NH+
4
�CNH+
4
�x+ LNH3Cl�
�CCl�
�x+ LNH3Na+
�CNa+
�x+ : : :
JNH+
4= LNH+
4NH3
�CNH3
�x+ LNH+
4NH+
4
�CNH+
4
�x+ LNH+
4Cl�
�CCl�
�x+ LNH+
4Na+
�CNa+
�x+ : : :
JCl� = LCl�NH3
�CNH3
�x+ LCl�NH+
4
�CNH+
4
�x+ LCl�Cl�
�CCl�
�x+ LCl�Na+
�CNa+
�x+ : : :
JNa+ = LNa+NH3
�CNH3
�x+ LNa+NH+
4
�CNH+
4
�x+ LNa+Cl�
�CCl�
�x+ LNa+Na+
�CNa+
�x+ : : :
......
......
...
(5)
To simplify this system the combined seawater ions are treated as one compound. Ammonia and
ammonium treated as two di�erent compounds in this section, however, as there are no means
to measure the two molecules separately, they are combined to one NHx �ux in the practical
work. Furthermore, it is assumed that the coupling coe�cients are negligible. Meaning that the
13
AU � Engineering Membrane
�ux of ammonium only is driven by the gradient of ammonium and not a�ected by the transport
of other seawater ions and vice versa. This reduces the problem to the three transport equations
seen in equation 6.
JSea = LSea
�CSea
�x
JNH3= LNH3
�CNH3
�x
JNH+
4= LNH+
4
�CNH+
4
�x
(6)
In this simpli�ed representation of the problem, each �ux depends on a membrane coe�cient,
the chemical gradient, and the membrane thickness. The aim of this set-up is to isolate NHx
from seawater. Complete isolation is hard to obtain as permeating NHx molecules will tend to
drag water and dissolved ions across the membrane with it. However, as long as a measurable
amount of NHx is allowed to pass the membrane while enough seawater ions are restrained to
prevent precipitation, the system is accomplishing its goals. In other words, a selectivity for NHx
is needed. The membrane thickness does not a�ect the selectivity as it is constant for all the
species. It is however important how fast the system equilibrates. The membrane coe�cient
is the key to selectivity as it represents how well the di�erent compounds di�use through the
membrane material. For instance, hydrophobic membranes are selective for non-ionic and non-
polar compounds as the structure of the membrane and the transported material generally have
similar physical characteristics.
The set-up investigated in this project, a hydrophobic membrane is used which would be selective
for ammonia transport whereas the seawater ions and ammonium �ux would be restrained.
Figure 7 show a representation where a hydrophobic membrane separates a seawater sample
and Milli-Q water acts as the recipient. In this case, the chemical gradients are �xed by the
seawater concentrations. An enrichment of NHx relative to seawater ions will happen as long
as LNH3is higher than LSea thus the membrane is selective for ammonia. The higher membrane
coe�cient allows ammonia to equilibrate faster than the other species.
Figure 7: Schematic representation of membrane transport in a hydrophobic membrane from seawater to
Milli-Q water. Arrows size indicate membrane coe�cient for the compound. Arrow direction
show direction of �ux. Green indicates favorable transport whereas red indicates undesirable
transport.
As the membrane constant for ammonia generally would be higher than for ammonium, it makes
sense to shift the concentration on one or both sides to ensure the highest ammonium gradient.
This is done by alkalizing the seawater sample to deprotonate the ammonium and use acid
as a recipient to protonate the transported ammonia. This con�guration is shown in �gure
14
AU � Engineering Membrane
8. As the seawater NHx concentration is shifted away from ammonium and the recipient NHx
concentration is shifted towards ammonium, the ammonium gradient will shift direction and force
some of the ammonium to di�use back into the sample. Though this di�usion is undesirable it
is minimized by the low membrane coe�cient for the ions. In this con�guration, the ammonia
gradient is close to the NHx concentration in the sample and the ammonium gradient close to
the NHx concentration in the recipient. The maximum concentration di�erence between the
sample and the recipient are restrained by the equilibrium between the ammonia and ammonium
�ux.
Figure 8: Schematic representation of membrane transport in a hydrophobic membrane from alkalized
seawater to acid. Arrows size indicate membrane coe�cient for the compounds. Arrow
direction show direction of �ux. Green indicates favorable transport whereas red indicate
undesirable transport.
JNH3= JNH+
4
LNH3
�CNH3
�x= LNH+
4
�CNH+
4
�x
LNH3
LNH+
4
=�CNH+
4
�CNH3
LNH3
LNH+
4
=CSample
Crecipient
(7)
As shown by the relation in equation 7 a higher selectivity for non-ionic compound will allow for
a higher sample concentration of NHx simultaneously slowing the contamination by seawater
ions.
4.2 Materials
The membrane testing rig, seen in �gure 9, was borrowed from the Electrochemical Energy
Conversion and Batteries group at Aarhus University. The rig utilizes a sandwich/pressure
system, allowing it to test any sheet membrane regardless of thickness and surface. Under
assembly four polymer rods were utilized to secure the alignment of the parts. The pressure
plates were connected with eight 6 mm steel bolts to apply the needed pressure to hold the rig
together and watertight. The spacers and �ow cells allowed for 2.1 ml volume on each side of
the membrane with a 25 cm2 membrane area. An even �uid �ow over the membrane area was
ensured by a ba�e con�guration on the �ow cell walls.
15
AU � Engineering Membrane
Figure 9: Schematic of the membrane testing rig
Four sintered PTFE membranes were tested, PMV10, PMV15, BM95 and BM100, all of them
supplied by Porex. These membranes were selected as they have the highest porosity and
smallest thickness of there product lines. The supplied material data can be found in appendix
D or at their website [33]. It appears by the product names that the membranes received are
sets of two samples from di�erent product lines. The exact di�erences have not been given by
Porex.
4.3 Method
To ensure su�cient saturation of solvents the membranes were pre-wetted with 96 % ethanol
for at least 24 h before they were tested. Each test set-up was prepared with the desired
membrane and sample concentrations and left to equilibrate for 10 to 12 h. This was done
to wash out all traces of ethanol and NHx. Varying quantity of NHx contamination from
handling the membranes under assembly proved di�cult to wash out. In the morning, in and
out�ow concentrations were measured either by conductivity measurement or the freshwater
OPA method.
The membrane testing rig was placed vertically with an upwards �ow on both sides to ensure
removal of any air pockets in the system. This lead to a co-�ow system con�guration, as the
ba�e con�guration in the �ow cells, were mirror images of each other. The �ow on both
sides was kept constant at 0.36 ml/min giving a retention time of 5.8 min. With the aim of
minimizing misplaced salt and NHx each �ow cell was assigned for either sample or receiving
liquid throughout the whole project.
4.4 Membrane transport
To measure the salt transport arti�cial seawater was used as the sample and demineralized water
as the recipient. The changes in concentration were measured using a conductivity meter. The
out�ow concentrations were used to calculate the permeability of the membrane, using equation
16
AU � Engineering Membrane
8, as precipitation of salts were seen in the sample in�ow tubing, but not in the out�ow or in
the �ow cell. The subscript s and r refers to sample and receiving solution respectively.
Cr;out
Cs;out + Cr;out
� 100 = T ransport% (8)
The ammonia transport was set-up with a NHx solution with known concentration in deminer-
alized water as the sample and either pure demineralized water or 0.1 M HCl as the recipient.
The NHx concentration was measured using the OPA method described in section 3 or using
a conductivity meter. The percentage of ammonia transported to the receiving solution was
calculated by the concentrations of in�ow sample and out�ow recipient.
Cr;out
Cs;in
� 100 = T ransport% (9)
The measured transport percentage is given in table 3 where the membranes are referred to by
their product code. Apart from PMV15 salt transport is roughly the same for all the membranes.
The NHx transport, however, is around 3 times higher in the BM series than for PVM. Using
an acidic recipient also increase the NHx transport, as predicted by the theory.
Membane PMV10 PMV15 BM95 BM100
Salt transport
Demineralised water 14.4 � 0.6 05.7 � 0.9 16.0 � 00.8 14.3 � 00.7
NHx transport
Demineralised water 01.9 � 1.8 11.5 � 2.3 34.0 � 05.8 37.1 � 15.3
0.1 M HCl 18.7 � 3.0 24.6 � 4.7 77.2 � 31.6 92.3 � 31.6
Table 3: Salt and NHx transport procentage in PTFE membranes with 95% con�dence interval.
4.5 Membrane selectivity
The membrane selectivity is de�ned as LNHx/LSea. This indicates the theoretical maximum
concentration increase of one species relative to an another in the membrane process. It is
possible to calculate the membrane coe�cients for the system by recognizing that the �ux is
the derivative of the concentration in the receiving solution.
dCr
dt=
L
�X(Cs � Cr) (10)
An assumption of constant molar concentrations is introduced, where the sum of CS and Cr is
noted as the contant a. Hereafter, the equation is integrated by separation of variables.
Cr = k � e�2 L
�Xt +
a
2(11)
The integration constant k can be determined by applying one set of boundary conditions. As
the receiving solution always is kept pure from the permeating species k is found to be �a=2,at the same time a is rede�ned as Cs;t0.
Cr =Cs;t0
2� Cs;t0
2� e�2 L
�Xt (12)
17
AU � Engineering Membrane
The membrane coe�cient can �nally be isolated by applying the set of boundary conditions at
t equals 5.8 min.
L = � �X
2t5:8ln
(1� 2Cr;t5:8
Cs;t0
)(13)
The calculated membrane coe�cients listed in table 4 con�rms the indications from the transport
calculations, where the BMmaterial is better suited for NHx permeability than the PMV material.
The BM100 membrane performed best according to the transport calculations and show the
best selectivity for NHx. Considering the NHx membrane coe�cient alone, the BM95 membrane
is superior. This deviation occurs as the membrane coe�cient accounts for membrane thickness
to evaluate only the material, whereas the transport calculation evaluates the e�ectiveness of
the complete set-up.
Membane PMV10 PMV15 BM95 BM100
Lsea [�m/min]3.80 1.86 6.00 3.78
(3.62 : 3.99) (1.54 : 2.21) (5.67 : 6.36) (3.55 : 4.02)
LNHx [�m/min]0.47 4.85 22.7 15.2
(0.01 : 1.28) (2.55 : 12.4) (10.2 : 0-0 ) (11.5 : 21.6)
LNHx/LNHx0.12 2.60 3.78 4.01
(0.00 : 0.35) (1.15 : 8.06) (1.60 : 0-0 ) (2.87 : 6.10)
Table 4: Salt and NHx membrane coe�cients and selectivity in PTFE membranes with 95% con�dence
interval.
4.6 Sensor response
A sensor signal will always have some delay in its response to changes in the monitored environ-
ment. To evaluate the membrane set-up as an ammonium sensor a step-test was conducted.
The BM100 membrane was used for this test as it has shown the highest NHx transport.
The sensor con�guration used in this project will as a minimum have a time delay equivalent to
the transport time between sample input and the �uorometric detection. If a complete turbulent
motion is maintained throughout the sensor as well as equal co-current �ow rates on both sides
of the membrane it is theoretically possible to preserve the concentration step signature in the
sensor signal with only a transport delay.
The majority of the sensor consists of peristaltic pump tubes with an inside diameter of 0.64
mm. The membrane testing rig was designed for higher �ow rates causing the in- and outlet
channel to be dimensioned at 4 mm in diameter and 10 cm in length. With a Reynold number
of 13000 for the peristaltic pump tubes �ow, the �ow is de�nitely turbulent. The inlet �ow in
the membrane testing rig, however, is in the transition zone between laminar and turbulent �ow
(1500-3000) with Reynold's number of 2100. [34]
A Simulink model was established to evaluate the measured step response. The mixed �ow in
the membrane rig inlets are not trivial to model and was therefore simpli�ed by assuming these
channels as stirred tank reactors. A more detailed description of the model is given in appendix
18
AU � Engineering Membrane
C. The model and data from the step-test are seen in �gure 10. The overall correlation is good,
especially considering the simpli�cations used in the model, yet the actual system takes about
10 min longer to equilibrate than predicted by the model. This delay probably occurs as the
concentration pro�le in the in- and outlet channels, in reality, is more complex than the assumed
uniform concentration applied in the model.
Figure 10: Step-test with the BM100 membrane. Two steps are included in the graph, where at t0 the
concentration were changed from 0 to 4.2 �M and at t60 from 4.2 to 0 �M.
19
AU � Engineering Chelating agents
5 Chelating agents
The concept behind the chelating agent approach is to add additional chemicals to the reagents
which can react with the sea salts ions to counteract precipitation. The goal is to stabilize
the sample to a degree where the �uorescence detection can be measured with the freshwater
set-up.
5.1 Theory
The nature of a chelating agent enables it to bind a cation in a complex, thus reducing the
concentration of free cations. An example is shown in �gure 11 where an EDTA molecule
interacts with a divalent cation to form a complex anion. In general, a chelating agent is an
organic molecule with multiple electron donor sites that stabilize the complex by creating one
or more chelating rings with the cation [27].
Figure 11: Structures of (a) EDTA, in its fully deprotonated form, and (b) in a six-coordinate
metal�EDTA complex with a divalent metal ion. [35]
In relation to seawater precipitation, chelating agents would form complexes with magnesium
and calcium ions. Following the example above producing [MgEDTA]2� and [CaEDTA]2�. Thus,
a chelating agent will lower the concentration of free magnesium and calcium ions. A su�cient
amount of chelating agent will hereby prevent precipitation as the ion concentrations are reduced
to below the solubility point.
5.2 Materials and method
The approach to this method was heavily based on a trial and error process. The initial test
aimed to verify various reagents compositions selected based on a literature search. This test
indicated a problem with the bu�er system. A bu�er experiment was conducted to �nd whether
phosphate, carbonate or boric acid would be the most suitable bu�er. Finally, the e�ect of
sodium citrate as a chelating agent was evaluated.
The mechanical set-up used correspond to the freshwater set-up outlined in section 3. The
chemical composition of the reagents was changed between each sample and is further outlined
in the continuation of the individual experiment description.
20
AU � Engineering Chelating agents
5.3 Initial test
Several sources were found claiming that they have discovered suitable con�gurations for chelat-
ing agents. Y. Liang et al. [10] used an EDTA solution as third reactant. This was tested in a
previous study [28]. EDTA was able to prevent precipitation, unfortunately, it also seemed to
a�ect the OPA reaction. L. Plant et al. [29] do not use the OPA method but try to detect NHx
by conductivity. However, they also had problems with precipitation and tested both EDTA and
sodium citrate, preferring the latter. Finally, N. Amornthammarong and J. Zhang [11] claim
that the precipitation can be avoided by increasing the sul�te concentration and omitting the
phosphate bu�er.
As EDTA already has been tested this work focus on citrate and the phosphate bu�er. Table
5 shows four selected reagent tests to express the �ndings. The tested reagent compositions
were named 'Citrate', 'Citrate bu�er', 'Sul�te 3' and 'Sul�te 10'.
The 'Citrate' solutions were derived from L. Plant et al. [29], as they do not use the OPA
method, OPA and sul�te were added in the concentrations used in the freshwater method. The
'Citrate + bu�er' is closely related to the 'Citrate' but phosphate bu�er is used to control the
pH. This was done to investigate the e�ect of the phosphate bu�er system. 'Sul�te 10' follows
the recipe published by N. Amornthammarong and J. Zhang [11]. To test the statement about
sul�te concentration being the main reason for prevented precipitation 'Sul�te 3' was produced
with a sul�te concentration at the same level as the freshwater method.
Citrate Citrate + bu�er Sul�te 3 Sul�te 10
OPA reagent
OPA 010 mM 010 mM 25 mM 25 mM
Sul�te reagent
Sul�te 003 mM 003 mM 03 mM 10 mM
Citrate 200 mM 200 mM
NaOH 075 mM
Solvent Mili-Q Phosphat bu�er Mili-Q Mili-Q
pH 11.7 10.3 9.3 10.1
Precipitation - + - -
Table 5: Overview of reagents in four initial precipitation tests. All the samples were mixed with equal
amounts of seawater, OPA reagent, and Sul�te reagent. Visible precipitation is indicated with
'+' and a clear liquid are indicated with '-'. pH was measured just after mixing the sample and
visible examination.
At �rst glance, the hypothesis of phosphate bu�er causing precipitation to seemed to hold.
Unfortunately, where the pH of 'Sul�te 3' and '10' measured to be lower than the 10.7 reported
by N. Amornthammarong and J. Zhang [11] and necessary for �uorometric detection. The two
'Sul�te' samples were therefore adjusted to pH 11 by 2.5 M sodium hydroxide to see how the
solutions performed at the expected pH. The result of this is shown in �gure 12. Only the
'Citrate' reagent composition showed no sign of precipitation when adjusted to the required
pH. The 'Citrate + bu�er' seems to produce the highest precipitation. The two 'Sul�te' tests
21
AU � Engineering Chelating agents
de�nitely produce some precipitation after pH adjustment, though it seems to produce less than
the 'Citrate + bu�er'.
(a) Citrate (b) Citrate bu�er (c) Sul�te 3 (d) Sul�t 10
Figure 12: Presipitation test in seawater with di�erent reagents, all test consist of equal amounts of
seawater, OPA reagent and Sul�te reagent
5.4 Bu�er solutions
The results from the initial test showed that it was possible to maintain a clear sample at pH 11
using citrate. However, utilizing phosphate bu�er caused precipitation. This behavior indicated
solubility limits with phosphates and lead to an investigation on bu�er solubility. Two alternative
bu�er systems were suggested; carbonate and boric acid. Solubility constants for boric acid were
not obtained and are therefore not present in table 6. The solubility of carbonates was found
to be magnitudes greater than for phosphates. However, the initial precipitation calculations on
seawater showed a supersaturation of carbonate both carbonate and boric acid were tested as
bu�er systems.
mol/l Phosphates Carbonates
[30] Ksp M Ksp M
Mg2+ 0.057 1:5 � 10�24 [36] 4:6 � 10�10 6:8 � 10�6 [27] 3:6 � 10�4Ca2+ 0.011 2:1 � 10�33 [27] � 2:0 � 10�13 4:9 � 10�9 [27] 1:3 � 10�6
Table 6: Saturation molarity for bu�er solutions at 298 K. Natural occurring carbonates are not included
in the calculation.
Two sul�te reagents with 0.25 M bu�er compound and 0.2 M citrate were prepared for the
two bu�er systems. Samples were prepared by mixing 12 ml of Red Sea seawater with 12 ml
OPA reagent before adding 12 ml sul�te reagent. This speci�c order was followed to minimize
precipitation chance by diluting the sample with OPA reagent. At room temperature, both
systems performed well. The samples were heated on a heat plate to simulate the heating coil.
The carbonate system started to precipitate at 53 �C and was quite cloudy at 57 �C. See �gure
13. The boric acid, on the other hand, kept clear until 98 �C, which was the highest temperature
tested.
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AU � Engineering Chelating agents
(a) Carbonate 50 �C (b) Carbonate 57 �C (c) Boric acid 20 �C (d) Boric acid 98 �C
Figure 13: Temperature presipitation test with 0.25 M carbonate or boric acid bu�er both containing
0.2 M citrate. First signs of precipitation in the carbonate bu�er were witnessed at 53 �C.
5.5 Citrate concentration
The impact of citrate was measured by preparing a series of sul�te reagents with varying citrate
concentration. All of the reagents were prepared with 0.25 M Boric acid and adjusted to pH 11
after addition of citrate. The sul�te reagents were tested in a sensor set-up similar to the initial
system in section 3. The OPA reagent was the same. A seawater sample form Aarhus bay (N
56.196518, E 10.265427 taken 14:30 the 29th of January 2019) was used as the sample, as
the Red Seawater salt was contaminated with too much NHx to give a meaningful reading.
The sensor response is seen in �gure 14. There is no 0 mM point present as this con�guration
clogged the system before the signal was stable. When visibly inspected, only the 0 mM con-
centration showed signs of cloudiness. Whereas the �uorometer detected a increase in signal
up to 200 mM, presumably due to precipitation. From a citrate concentration of 200 mM and
upwards the signal seemed stable.
Figure 14: Series of variation in citrate concentration using the OPA method. Error bars indicate 95 %
con�dence interval.
23
AU � Engineering Chelating agents
5.6 Sensor response
A step-test was conducted to evaluate how the chelating agent approach would perform as a
sensor. By the same arguments as for the membrane set-up, the sensor signal will be able to
follow the NHx concentration exactly, only with a time delay, if a turbulent �ow is maintained
throughout the tubing of the set-up. As this set-up only apply peristaltic pump tubes, the �ow
is de�nitely turbulent with a Reynold's number of 13000, as calculated in section 4.6.
The time delay was found to be approximately 2 min by following an air bubble through the
sensor. Figure 15 show the response of the �uorometric signal when the sample concentration
is changed from 0 to 2.25 �M NHx and back. The concentration step is seen in the signal
but is not maintained completely as the sensor signal needs an extra minute to equilibrate. In
this con�guration, the sensor is able to equilibrate within 3 min of a concentration change. In
a monitoring application the 2 min time delay would be taken into account, which allows for a
measuring frequency of 1 sample per min.
Figure 15: Step-test with chelating agent. Two steps are included in the graph at t0 the concentration
were changed from 0 to 2.3 �M and at t5 from 2.3 to 0 �M.
24
AU � Engineering Seawater OPA method
6 Seawater OPA method
The proposed method for seawater measuring is based on the chelating agent approach. The
step-test showed a faster and precise response compared to the membrane set-up. The me-
chanical outline follows the initially proposed sensor in section 3.
1 L of OPA reagent was prepared by dissolving 1.340 g of OPA in 200 ml of 96 % ethanol. The
solute was then diluted to 1 L with Mili-Q water.
1 L of sul�te reagent was made by combining 15.46 g of boric acid, 58.82 g of trisodium citrate
and 5 ml 24% formaldehyde in 900 ml Mili-Q water. The solution was adjusted to pH 12 with
3 M sodium hydroxide. 0.378 g of sodium sul�te was combined with the bu�er solution in a 1
L volumetric �ask and the �nal volume was adjusted to 1 L.
The sample was mixed with the OPA reagent before the sul�te reagent was added. This order
was strictly maintained to prevent pH and concentration peaks to initiate precipitation in the
sample. Both sample and reagents were continuously supplied by an Ole Dich peristaltic pump
at a rate of 0.36 ml/min, corresponding to speed 4.0 on the pump. The combined solution was
passed through the Supertherm thermostat from Mikrolab Aarhus set to 75 �C for 35 seconds.
Finally, the �uorescent yield was detected by the Perkin-Elmer LS-2 �lter �uorimeter set to 425
nm and recorded to a laptop using an Arduino Uno.
6.1 Calibration
To produce a reliable standard series for seawater measurements both Red Sea arti�cial seawater
and NHx cleaned seawater supplied by the Department of Environmental Science in Roskilde
were tested. Both candidates were rejected as they were clearly contaminated. Instead, the
method was calibrated with a pure water standard series also supplied by the Department of
Environmental Science. Assuming that the absence of dissolved and complexed sea salts would
not impact the �uorescence intensity of the sample. To minimize the con�dence interval the
calibration was performed �ve times.
Figure 16: Calibration of the seawater OPA method with 95% con�dence intervals using a pure water
standard series
25
AU � Engineering Seawater OPA method
The calibration gave a lower detection level of 0.06 �M NHx, calculated by 3 times the standard
deviation of the zero-sample. The higher detection limit is restricted by the working range of the
�uorometer, in this calibration 3.5 �M NHx. The highest 95% con�dence interval calculated
were 0.01 �M NHx around 0 and 3.5 �M.
6.2 pH e�ect
The lack of sea salts may not directly a�ect the �uorescence but it will a�ect the bu�er capacity
of the sample and hereby the �nal pH of the solution. pH is known to in�uence the �uorescence
signal so the absence of sea salt bu�er capacity indirectly a�ects the measurements. To accom-
modate for this in the calibration the e�ect of a pH shift from 10 to 11.2 was investigated. This
was done by measuring the �uorescence signal and pH of the �nal solution while the standards
were slowly acidi�ed.
It was done by equilibrating the sensor for 5 min, starting with 100 ml volume of standard around
11.2 pH. The �uorescence signal was monitored for a further 5 min while the solution was col-
lected for pH analyses. Then the standard was acidi�ed by adding 20 �l fuming hydrochloric
acid. Concentrated acid was used to minimize volume change of the standard. This process was
repeated until the pH of the measured solution were below 10.2. This was done for standards
of 0, 0.71 and 1.43 �M NHx.
To evaluate the di�erent standards as one, each measurement was scaled so that the �uores-
cence signal at pH 10.5 was �xed at 1. As none of the samples were measured exactly at pH
10.5 this value was estimated by linear regression of all samples within pH 10.4 to 10.6.
Figure 17: Change in �uorescence signal as response to pH. Blue points show 0.71 and 1.43 �M NHx
standards. Orange points show 0 �M NHx standard. See text for details on regression line.
First signi�cant observation of �gure 17 is that the 0 �M NHx standard follow the trend by the
NHx containing samples. This indicates NHx contamination of either the reagents or the sample.
An ammonium free solution cannot produce any 2H-Isoindole-1-sulfonate so the �uorescence
signal should not be in�uenced by pH changes or at least not in the same way as ammonium
containing solutions. Contamination of the reagents can be included in the calibration as long
as they are stable.
26
AU � Engineering Seawater OPA method
In regard to the �uorescence signal response to pH changes, the signal seems stable between pH
values of 9.8 and 10.5 whereafter the signal decreases with around 30 % at 11.2. The regression
line in �gure 17 is composed of a constant form 9.8 to 10.5 where after a polynomial function
of second degree is �tted to the points between 10.5 to 11.2. This approach was chosen as no
theoretical function are associated with the pH and �uorescence signal correlation.
27
AU � Engineering Amines
7 Amines
The investigation on amine interference was limited to the three methylamines. Using the scan
setting on the Perkin-Elmer the emission spectra of the amines, an NHx and a blank solution were
recorded. Each spectrum was recorded 3 times and the emission values for each wavelength, to
nearest nm, were average together using excel. The settings and reagents from the seawater
sensor, section 6, were used in this process. Figure 18 show the average of the three readings
for the amines and the NHx solution, all of them after subtraction of the blank spectra. Both
dimethylamine and trimethylamine showed no interference. Methylamine, on the other hand,
shows a small interference. By assuming linearity the interference of methylamine at 425 nm,
was calculated, to 0.035 % when the concentration di�erence is taken into account.
Furthermore, the methylamine spectra is revealing a secondary peak at 520 nm, which is not
present in the NHx spectrum. This feature theoretically enables the detection of both NHx
and methylamine in the same sensor by applying a second �uorometer measuring at 520 nm.
By measuring the signal at 425 nm and 520 nm simultaneously the concentrations of NHx
and methylamine can be calculated using the shift in the signal ratio for the two components.
However, this requires a very precise sensor because the methylamine concentration is expected
to be below 50 nM [21, 22] and because the noise will be ampli�ed by the additional measuring
point required.
Figure 18: Emission spectra of methylamines at 1 mM and NHx at 2.3 �M all corrected with an blank
spectra.
Additional amine spectrums were produced with concentrations of 100 mM. The raw spectra
along with a blank are shown in �gure 19. In this set-up is the amine concentration 10 times
higher than the OPA concentration to push the reaction equilibrium towards the OPA-sul�te-
amine product.
The trimethylamine spectra follow the blank more or less, indicating once again that trimethy-
lamine dos do not react with OPA. Both the mono- and dimethylamine spectra show signi�cant
lower emission than the blank. If at the same time the similarities between the blank and the
NHx spectra, in �gure 18, is considered. It seems evident that the reagents were contaminated
28
AU � Engineering Amines
with NHx and that the low mono- and dimethylamine emissions occur as the excesses of amines
depletes the OPA reagent before it reacts with the ammonia.
Figure 19: Raw emission spectra of methylamines at 100 mM and the blank spectra.
Generally, this investigation suggests that methylamine is capable of reacting with OPA and
sul�te to produce a �uorescence compound with much less intensity then ammonia. However,
introducing a small secondary peak at 520 nm. The two products are compared in �gure 20, it
is assumed that the addition of a methyl group on the nitrogen atom changes the conjugation
of the two ring structures and hereby alter the �uorescent characteristics. Dimethylamine can
react with OPA but do not produce a �uorescence compound. Possibly because the second ring
structure is unable to close with one bond to the nitrogen. Trimethylamine seems to be inert
to the reaction.
Figure 20: To the left the OPA-Sul�te-Ammonia product 2H-Isoindole-1-sulfonate. To the right the
proposed OPA-Sul�te-Methylamine product.
29
AU � Engineering Monitoring test
8 Monitoring test
The set-up outlined in section 6 were moved to Kattegatcenteret in Grenå with the goal of
measuring daily variations in NHx concentration. Unfortunately were there seawater intake
broken down doing the measuring period so it was not possible to measure on Kattegat seawater
concentrations. The instrument was instead deployed to measure on the tropical quarantine
aquarium.
The equipment was set to measure for 2 runs of 4 days. The volume of reagent, stored in 2 L
blue-cap bottles, was the limiting factor for deployment time. In order to reduce the amount of
data to a manageable size, every block of 50 readings was averaged to a single measurement
point. This led to a sampling time of approximately 53 seconds with each sample being the
average of 50 individual readings within that period.
Preparation of reagents was done in one 5 L batch. Unfortunately did the pH-meter broke
down during the preparation resolving in an over-adjustment of the sul�te reagent. The pH
was measured to 12.58 after the deployment. Fortunately did the pH of the �nal reagent and
sample mixture fell within the tested pH range in �gure 17 with a pH of 10.93.
The sensor output was below the calibrated zero-point throughout the measuring period. The
set-up was therefore tested at Kattegatcenteret with a sample of Mili-Q water. This showed a
zero reading of 0.0025 V, after pH adjustment of the signal according to �gure 17, compared to
0.15 V at calibration. It was assumed that this o�set occurred due to lack of NHx contamination
in the reagents. The aquarium concentration was therefore calculated by shifting the calibration
curve downwards to suit the Milli-Q sample while the slope was maintained.
Figure 21 show the two measurement periods. The �rst period terminated a day too early due
to a computer failure ending the data logging. The mechanical part of the set-up showed no
sign of wear and tear and was running throughout the 8 days of measuring without replacement.
With the exception of the 6th and 7th oscillated the NHx concentration in the aquarium between
0.04 and 0.08 �M almost on a daily basis, which is just around the lower detection limit of the
sensor.
Figure 21: NHx concentration in the tropical quarantine aquarium. t0 corresponds to 00:00 at the �rst
date of measuring (UTC+2).
30
AU � Engineering Discussion
9 Discussion
The investigation of solubility products veri�es the idea that magnesium and calcium are the
main cations responsible for precipitation in the samples. Both of them is able to precipitate
with several anions showing the need for carefully choosing reagent compositions.
The aim of the membrane approach was to separate NHx form magnesium and calcium by
membrane �ltration. The best scenario obtained, lowered the salt concentration to 15 % of
the original value while capturing 90 % of the NHx. Those numbers generally imply an accept-
able membrane separation, however, considering the very low solubility product of magnesium
hydroxide, 3�10�5 % of the original magnesium concentration is theoretically enough to cause
precipitation at pH 11. Only the combined salt conductivity was measured in the transport
experiment meaning that the membrane resistance for divalent cations very well could be higher
than the mean salt retention.
One additional challenge for the membrane process which has not been addressed in the report
is possible problems with biofouling. This phenomenon arises when untreated seawater is passed
over the membrane surface where algae can attach to the membrane and clog this as they grow.
Besides the negative e�ects on membrane performance is the incubation of biomass inside the
sensor troublesome as it surely will change the NHx concentration. Biofouling can be reduced
by a number of actions mostly pretreatment of the membrane or chemical cleaning when in use.
One process that �ts well with this set-up is to raise the alkalinity of the seawater in order to
stress the algae survival abilities, which simultaneously improve the NHx transport [37].
By carefully choosing the bu�er and chelating agents it was possible to avoid precipitation in
the sample. However, multiple reported reagent compositions were tested but did not prevent
precipitation in the seawater used in this project. This indicates that the variation in seawater
composition hinders the use of one single procedure for all waters in the world. This also
means that the method obtained in this report should be tested in di�erent waters to verify its
robustness.
Comparing the membrane and chelating agents sensor response proved that the more technical
membrane set-up reacted around 20 times slower than the chelating agent set-up. It should
be possible to improve the slow response of the membrane by using redesigned �ow cells and
thinner membranes. Although the complications of the membrane process can be optimized to
some extent it is generally assessed that the technical complexity of a membrane separation
does not pay o� in respect to chemical simpli�cation or robustness of the sensor. The chelating
agent approach is therefore recommended.
The established seawater sensor obtained a range from 60 nM to 3.5 �MNHx with an uncertainty
of 10 nM. This range includes the vast majority of seawater measurements reported by Johnson
et al. [2]. However, to accommodate especially the Arctic regions a lover detection limit below
10 nM NHx should be obtained. An uncertainty of 10 nM is quite considerable in regard to the
expected concentrations and should be the immediate aim for optimization in future work.
Doing test deployment the sensor succeed in monitoring NHx on an online set-up for almost
two tests of four days, only interrupted by a software error in the �rst period. The data were
measured with a sampling rate of 1 HZ and logged as averages of 50 samples. The limiting
factor for deployment time where the volume of reagent containers, here 2 L blue-cap bottles.
31
AU � Engineering Discussion
Two general challenges for the OPA method is performing a reliable calibration and constant
reagent consumption. The issue with calibration is a result of the omnipresence of ammonia.
It was possible to produce su�cient ammonia free water by applying a Milli-Q purifying station
to the demineralized water supply in the building. It was not possible, however, to produce
calibration standards without clear external NHx contamination. The excess NHx origin could be
contaminated glassware, airborne ammonia or form handling the solutions. In the end, standard
solutions from an NHx-pure lab in Roskilde were used to calibrate the set-up. Even though these
standards showed good precision, the later seawater standards were clearly contaminated form
transport, questioning the accuracy of this method. This lack of stable NHx solutions make it
impossible to perform trustworthy calibrations on site and therefore hard to asses sensor drift.
The challenge of reagent consumption mainly lies in the possible sensor drift by contamination of
reagents. The method developed in this report utilizes 0.5 L of each reagent per day deployed.
At test-deployment, the reagents were changed every fourth day. Longer periods could be
obtained by using larger reagent containers, but this would also increase the working time of
each container and hereby the chance of NHx di�usion into the reagents. Furthermore, there
is an economic challenge to using reagents the price of chemicals to run the proposed set-up is
estimated to 1 $/day, see Appendix E. In addition to this is transport and man hours cost which
could be substantial especially in remote area monitoring.
The interference test of amines showed a relative signal of 0.035 % for methylamine and no
interference from di- and trimethylamine. Which is lower than the expected 0.2 % [13]. This
increased selectivity for NHx can only be caused by the reagent composition, even though no
means were taken to improve upon this feature.
In the analysis of emission spectra showed methylamine an extra �uorescence peak at 520 nm.
Theoretically, this allows for the detection of both NHx and methylamine, or primary amines,
within the same sample using the OPA method. However, this would require an extremely
sensitive sensor due to the expected low amine concentration and the relatively low signal
compared to the signal of NHx.
The amine spectra also revealed that dimethylamine can react with OPA but dos not produce a
�uorescence compound. This reaction could prove bene�cial in determining NHx contamination
in reagents because a concentrated dimethylamine sample would outcompete the NHx reaction
and thereby produce a pure zero signal. The NHx contamination in reagents can, therefore, be
estimated by comparing the signal of a concentrated dimethylamine sample with a Milli-Q water
sample, shoving the true zero-point and the contaminated value respectively.
32
AU � Engineering Conclusion
10 Conclusion
The addition of membrane separation to the sample inlet did remove 85 % of the sea salt,
according to conductivity measurements, while capturing up to 90 % of the NHx concentration.
The sensor response of the membrane set-up was quite slow, around 40 minutes to reach
equilibrium, most likely due to the �ow cell design. Even though a redesign of the �ow system is
expected to raise performance considerably is the overall achievement not enough to challenge
the cleating agent method.
None of the seawater reagents found in the literature were able to prevent precipitation in the
seawater samples used in this project. Suitable reagent composition was obtained by changing
the bu�er to boric acid. The online sensor designed with these reagents was calibrated to mea-
sure between 0.06 to 3.5 �M NHx with an uncertainty of 0.01 �M. This range �t the expected
majority of seawater concentrations, however, this should be expanded to accommodate the
extremes. The deployment test showed good working conditions, but highlighted the limitations
on long term monitoring mainly being reagent consumption due to transport and chemical cost.
While the electronics showed high reproducibility between the same samples the change of
reagents were generally associated with signal �uctuations. Probably due to di�erent levels of
NHx contamination in the reagents. The main issue with the method is performing a trustworthy
calibration and measure the unavoidable contamination of reagents.
The investigation on amines showed a theoretical ability to measure methylamine with an addi-
tional �uorometric detection. Furthermore, the reaction of dimethylamine with OPA indicate a
zero-point measurement which could prove useful to estimate reagent contamination.
The online sensor con�guration is ready to use and has proven capable of monitoring NHx with
a time resolution of less than a minute. The reagent composition, however, should be tested
in a larger variety of seawater sites to prove its robustness towards changes in trace element
concentrations.
The reagent consumption will always be a limitation to the OPA method but can be minimized
by optimizing the �ow characteristics for the speci�c working condition. The continuous �ow
con�guration used here is best suited for trajectory or process work where the NHx concentration
is expected to change within short time periods. For a stationary monitoring system where the
NHx concentration is not expected to change rapidly, it would be bene�cial to develop a discrete
sampling system. This approaches will conserve reagents and prolong the possible deployment
time with the cost of time resolution.
33
AU � Engineering References
References
[1] P. A. Wheeler and S. A. Kokkinakis. Ammonium recycling limits nitrate use in the oceanic
subarctic paci�c. American Society of Limnology and Oceanography, 35:1267�1278, 1990.
doi: 10.4319/lo.1990.35.6.1267.
[2] M. T. Johnson, P. S. Liss, T. G. Bell, T. J. Lesworth, A. R. Baker, A. J. Hind, T. D.
Jickells, K. F. Biswas, E. Malcolm, S. Woodward, and S. W. Gibb. Field observations of
the ocean-atmosphere exchange of ammonia: Fundamental importance of temperature as
revealed by a comparison of high and low latitudes. Global Biogeochemical Cycles, 22:
GB1019, 2008. doi: 10.1029/2007GB003039.
[3] O. Boucher, D. Randall, P. Artaxo, C. Bretherton, G. Feingold, P. Forster, V.-M. Kerminen,
Y. Kondo, H. Liao, U. Lohmann, P. Rasch, S.K. Satheesh, S. Sherwood, B. Stevens, and
X.Y. Zhang. Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change,
chapter Chapter 7: Clouds and Aerosols, pages 571�657. 2013.
[4] Marc Roth. Fluorescence reaction for amino acids. Analytical chemistry, 43:880�882,
1971. doi: 10.1021/ac60302a020.
[5] Z. Genfa and P. K. Dasgupta. Fluorometric measurement of aqueous ammonium ion in a
�ow injection system. Analytical chemistry, 61:408�412, 1989. doi: 10.1021/ac00180a006.
[6] C. Molins-Legua, S. Meseguer-Lloret, Y. Moliner-Martinez, and P. Campins-Falcó. A guide
for selecting the most appropriate method for ammonium determination in water analysis.
Trends in Analytical Chemistry, 25:282�290, 2006. doi: 10.1016/j.trac.2005.12.002.
[7] A. M. Johnston, C. M. Scrimgeour, H. Kennedy, and L. L. Handley. Isolation of ammonium-
n as 1-sulfonato-iso-indole for measurement of d15n. Rapid Communications in Mass
Spectrometry, 17:1099�1106, 2003. doi: 10.1002/rcm.1029.
[8] H. Hu, Y. Liang, S. Li, Q. Guo, and C. Wu. A modi�ed o-phthalaldehyde �uorometric
analytical method for ultratrace ammonium in natural waters using edta-naoh as bu�er.
Journal of Analytical Methods in Chemistry, 2014:7, 2014. doi: 10.1155/2014/728068.
[9] L. Irving. The precipitation of calcium and magnesium from seawater. Journal of the
Marine Biological Association, 14:441�446, 1926.
[10] Y. Liang, C. Yan, Q. Guo, J. Xu, and H. Hu. Spectrophotometric determination of am-
monia nitrogen in water by �ow injection analysis based on NH3-o-phthalaldehyde-Na
2SO
3
reaction. Analytical Chemistry Research, 10:1�8, 2016. doi: 10.1016/j.ancr.2016.10.001.
[11] N. Amornthammarong and J. Zhang. Shipboard �uorometric �ow analyzer for high-
resolution underway measurement of ammonium in seawater. Analytical Chemistry, 80:
1019�1026, 2008. doi: 10.1021/ac701942f.
[12] R. M. Holmes, A. Aminot, R. Kérouel, B. A. Hooker, and B. J. Peterson. A simple and
precise method for measuring ammonium in marine and freshwater ecosystems. Canadian
Journal of Fisheries and Aquatic Sciences, 56:1801�1808, 1999.
34
AU � Engineering References
[13] R. Khouel and A. Aminot. Fluorometric determination of ammonia in sea and estuarine
waters by direct segmented �ow analysis. Marine Chemistry, 57:265�275, 1997. doi:
10.1016/S0304-4203(97)00040-6.
[14] Y. Zhu, D. Yuan, Y. Huang, J. Ma, and S. Feng. A sensitive �ow-batch system for on board
determination of ultra-trace ammonium in seawater: Method development and shipboard
application. Analytica Chimica Acta, 794:47�54, 2013. doi: 10.1016/j.aca.2013.08.009.
[15] D. J. Kearney, T. Hubbard, and D. Putnam. Breath ammonia measurement in helicobacter
pylori infection. Digestive Diseases and Sciences, 44:2523�2530, 2002. doi: /10.1023/A:1020568227868.
[16] J. M. Hales and D. R. Drewes. Solubility of ammonia in water at low concentrations.
Atmospheric Environment, 13:1133�1147, 1967. doi: /10.1016/0004-6981(79)90037-4.
[17] S. W. Brusilow and E. H. Gordes. Ammonia secretion in sweat. American Journal of
Physiology, 214:513�517, 1968. doi: /10.1152/ajplegacy.1968.214.3.513.
[18] N. Wajsbrot, A. Gasith, A. Diamant, and D. M. Popper. Chronic toxicity of ammonia to
juvenile gilthead seabream sparus aurata and related histopathological e�ects. Journal of
Fish Biology, 42:321�328, 1993. doi: /10.1111/j.1095-8649.1993.tb00336.x.
[19] R. D. Handy and M. G. Poxton. Nitrogen pollution in mariculture: toxicity and excretion of
nitrogenous compounds by marine �sh. Reviews in Fish Biology and Fisheries, 3:205�241,
1993. doi: /10.1007/BF00043929.
[20] B. Horstkottea, C. M. Duartea, and V. Cerdàb. A miniature and �eld-applicable multi-
pumping �ow analyzer for ammonium monitoring in seawater with �uorescence detection.
Talanta, 85:380�385, 2011. doi: 10.1016/j.talanta.2011.03.078.
[21] C. H. L. Cree, R. Airs, S. D. Archer, and M. F. Fitzsimons. Measurement of methylamines in
seawater using solid phase microextraction and gas chromatography. Analytical chemistry,
16:411�420, 2018. doi: 10.1002/lom3.10255.
[22] A. Aminot and R. Kerouel. The determination of total dissolved free primary amines in
seawater: Critical factors, optimized procedure and artefact correction. Marine Chemistry,
98:223�240, 2006. doi: 10.1016/j.marchem.2005.07.005.
[23] T. Olenius, R. Halonen, T. Kurtén, H. Henschel, O. Kupiainen-Määttä, I. K. Ortega, C. N.
Jen, H. Vehkamäki, and I. Riipinen. New particle formation from sulfuric acid and amines:
Comparison of monomethylamine, dimethylamine, and trimethylamine. JGR: Atmospheres,
122:7103�7118, 2017. doi: /10.1002/2017JD026501.
[24] L. L. Sørensen, K. Granby, H. Nielsen, and W. A. H. Asman. Di�usion scrubber - a
technique for measuring ammonia. NERI Technical Report No. 99, 99:1�35, 1994. ISSN
0905815X.
[25] T. DoMinh, A. L. Johnson, J. E. Jones, and Jr P. P. Senise. Reactions of phthalaldehyde
with ammonia and amines. Journal of Organic Chemistry, 42:4217�4221, 1976.
[26] E. Kulla and P. Zuman. Reactions of orthophthalaldehyde with ammonia and 2-
aminoethanol. Organic & Biomolecular Chemistry, 6:3771�3780, 2008. doi: 10.1039/b807714m.
35
AU � Engineering References
[27] C. E. Housecroft and E. C. Constable. Chemistry. 2010. ISBN 9780273715450.
[28] S. Læsaa. In situ measurement of ammonium in marine waters. Technical report, Depart-
ment of Engineering, Aarhus University, 2018.
[29] J. A. Needoba J. N. Plant, K. S. Johnson and L. J. Coletti. Nh4-digiscan: an in situ
and laboratory ammonium analyzer for estuarine, coastal, and shelf waters. Limnology and
Oceanography: Methods, 7:144�156, 2009. ISSN 1541-5856.
[30] Lenntech. Composition of seawater. www.lenntech.com/composition-seawater.htm.
[31] H. Strathmann. Ion-Exchange Membrane Separation Processes, volume 9 of Membrane
Science and Technology Series, chapter Chapter 2: Electrochemical and Thermodynamic
Fundamentals, pages 23�87. 2004.
[32] S. Kjelstrup and D. Bedeaux. Non-Equilibrium Thermodynamics of Heterogeneous Sys-
tems, volume 16 of Series an Advances in Statistical Mechanics, chapter Chapter 2:
Why Non-Equilibrium Thermodynamics?, pages 7�14. World Scienti�c, 2008. doi:
10.1142/6672.
[33] Porex. Polytetra�uoroethylene (porex virtek ptfe). www.porex.com/technologies/
materials/porous-plastics/polytetrafluoroethylene/.
[34] K. H. Cement, P. Fangel, A. D. Jensen, and K. Thomsen. Kemiske enhedsoperationer,
chapter Chapter 2: Væske- og Gasstrømning. 2009. ISBN 8750209418.
[35] David Harvey for Chemistry LibreTexts. 9.3: Complexation titrations. chem.libretexts.
org/Bookshelves/Analytical_Chemistry/Book%3A_Analytical_Chemistry_2.0_
(Harvey)/09_Titrimetric_Methods/9.3%3A_Complexation_Titrations.
[36] Aqion. Solubility product constants ksp at 25�c. www.aqion.de/site/16.
[37] A. Matin, Z. Khan, S. M. J. Zaidi, and M. C. Boyce. Biofouling in reverse osmosis
membranes for seawater desalination: Phenomena and prevention. Desalination, 281:1�
16, 2011. doi: /10.1016/j.desal.2011.06.063.
[38] R. A. Johnson. Probability and Statistics for Engineers, chapter Chapter 11: Regression
Analysis. 2014. ISBN 9781783992997.
[39] chembid. www.chembid.com/en/.
[40] Sigma aldrich. www.sigmaaldrich.com/catalog/product/mm/111037?lang=en&
region=DK.
36
AU � Engineering Derivation of carbonate precipitation equation
A Derivation of carbonate precipitation equation
The carbonate bu�er equilibriums control the protonation of carbonate species in relation to
pH.10�pH
10�pKa;1=
[H2CO3]
[HCO�
3 ]
10�pH
10�pKa;2=
[HCO�
3 ]
[CO2�3 ]
The �rst step in the derivation is to express a relation between the concentration of deprotonated
carbonate, the complete carbonate concentration and pH.
[CO2�3 ]
[CO3;tot ]=
[CO2�3 ]
[H2CO3] + [HCO�
3 ] + [CO2�3 ]
=1
[H2CO3]
[CO2�3 ]
+[HCO�
3 ]
[CO2�3 ]
+[CO2�
3 ]
[CO2�3 ]
=1
[H2CO3]
[HCO�
3 ]� [HCO
�
3 ]
[CO2�3 ]
+[HCO�
3 ]
[CO2�3 ]
+ 1
=1(
[H2CO3]
[HCO�
3 ]+ 1
)[HCO�
3 ]
[CO2�3 ]
+ 1
=1(
10�pH
10�pKa;1+ 1
)10�pH
10�pKa;2+ 1
Then the pH is isolated as the overall aim is to gain a pH point for precipitation.
[CO2�3 ]
[CO3;tot ]=
1(10�pH
10�pKa;1+ 1
)10�pH
10�pKa;2+ 1
[CO3;tot ]
[CO2�3 ]
=
(10�pH
10�pKa;1+ 1
)10�pH
10�pKa;2+ 1
[CO3;tot ]
[CO2�3 ]
=1
10�pKa;2� 1
10�pKa;1(10�pH)2 +
1
10�pKa;210�pH + 1
At this point is an introduction of constants used to ease the overview of the calculation.
Furthermore is a quadratic formula introduced.
[CO2�3 ]
[CO3;tot ]� 1 = Y
1
10�pKa;2= a
1
10�pKa;1= b 10�pH = X
37
AU � Engineering Derivation of carbonate precipitation equation
(pabX +
pa
2pb
)2
= abX2 +a
4b+ aX
This is used to isolate X.
Y = abX2 + aX
Y =
(pabX +
pa
2pb
)2
� a
4b
√Y +
a
4b=pabX +
pa
2pb
√Y +
a
4b�
pa
2pbp
ab= X
The constants are substituted and pH is isolated.
10�pH =
√√√√√√√ [CO2�3 ]
[CO3;tot ]� 1 +
1
10�pKa;2
41
10�pKa;1
�
√1
10�pKa;2
2
√1
10�pKa;1√1
10�pKa;2� 1
10�pKa;1
10�pH =
√√√√ [CO2�
3 ]
[CO3;tot ]� 1 +
4 � 10�pKa;1
10�pKa;2� 2
p10�pKa;1p10�pKa;2
p10�pKa;2 � 10�pKa;1
pH = � log
√√√√ [CO2�
3 ]
[CO3;tot ]� 1 +
4 � 10�pKa;1
10�pKa;2� 2
p10�pKa;1p10�pKa;2
p10�pKa;2 � 10�pKa;1
Finally is the carbonate concentration is substituted with the solubility equation for divalent
ions. The function then gives the precipitation pH as a function of the concentration of total
carbonate and divalent cations.
pH = � log
√√√√√√ Ksp
[M2+]
[CO3;tot ]� 1 +
4 � 10�pKa;1
10�pKa;2� 2
p10�pKa;1p10�pKa;2
p10�pKa;2 � 10�pKa;1
38
AU � Engineering Statistics
B Statistics
B.1 Regression analysis
The calibration was �tted to a straight line using the least square method. This was done by
following the outline in Miller & Freund's 'Probability and Statistics for Engineers' [38]. Firstly
is the three least squares estimators calculated.
Sxx =n∑
n=1
(xi � x)2 Syy =n∑
n=1
(yi � y)2 Sxy =n∑
n=1
(xi � x) � (yi � y)
Then the regression constants are given as below. Notice that a is the intercept and b is the
slope.
a = y � b � x b =Sxy
Sxx
The standard error of the estimate is calculated with the aim of estimating the con�dence
intervals of the regression.
se =
√√√√√√Syy � (Sxy)2
Sxx
n � 2
It is possible to calculate con�dence intervals for the intercept and slope, but for this application,
it is more relevant to evaluate on the con�dence interval for y.
(y0)� t�=2 � se√1
n+
(x0 � x)2
Sxx
The Student's t-distribution (t�=2) can be obtained by the TINV excel function. The degrees
of freedom is, in this case, n� 2. Notice that the subscript 0 refers to a single measurement or
point on the x or y axis.
B.2 Cin�dance interval for membrane transport
The uncertainty estimate for the membrane transport calculations is done by following the order
of operations.
The addition or subtraction rule de�nes that for two numbers with associated uncertainties are
the uncertainties added together.
a � �a + b � �b = a + b � �a + �b
The multiplication rule de�nes that for two numbers with associated uncertainties there are
multiplied or divided are the relative uncertainties added together to a relative uncertainty.
a � �a
b � �b=
a
b� a
b�(�a
a+
�b
b
)
39
AU � Engineering Statistics
B.3 Con�dance interval for membrane selectivity
The uncertainty estimate for the membrane coe�cient is complicated by the use of logarithms
in the calculation. The challenge with logarithms in uncertainty estimates is their non-linearity.
Meaning that a symmetric con�dence interval would not maintain its symmetry when applied
to a logarithmic function.
An uncertainty estimate for any function can be obtained by using the derivative of the function
multiplied with the uncertainty. The line of thought behind this approach is that the derivative
expresses the stability of the function to a change and the uncertainty express the statistical
boundaries for change. However, these assumptions are only valid as long as the derivative is
linear within the uncertainty boundaries.
f (a � �a) � f (a)� jf 0(a)j � �a
For the natural logarithmic function is the derivative 1/x.
ln(a � �a) � ln(a)� �a
a
The uncertainties in this case, especially for NHx measurements, were assessed to be too large
to uphold the assumption of linearity. The con�dence intervals are in this case calculated by
applying the uncertainty extremities in the calculation to obtain the con�dence interval for the
membrane coe�cient.
(� �X
2T5:8ln
(1� 2(Cr;t5:8 � �Cr;t5:8)
Cs;t0 + �Cs;t0
): � �X
2T5:8ln
(1� 2(Cr;t5:8 + �Cr;t5:8)
Cs;t0 � �Cs;t0
))
40
AU � Engineering Simulink model of the membrane sensor
C Simulink model of the membrane sensor
The Simulink model is seen in �gure 22. The model consists of two tank reactor functions,
marked with blue. The membrane transport described by equation 12 are implemented in the
orange area with the addition of a time delay to account for the retention time. The response
of the OPA method is assumed to be negligible compared to the membrane response. The
detection response of the OPA method is therefore modeled only by a time delay, indicated by
the green line.
Figure 22: Simulink model of the membrane sensor.
Figure 23: Tank model
The tank model represents a bu�er system for concentration
change. An inlet �ow with concentration Ci is accumulated in a
holding tank of volume V . The tank and out�ow concentrations
are identical C. In this case, is the tank (inlet to the membrane)
completely �lled with solvent so in- and out�ow are identical and
constant Q. A concentration shift in Ci will be "bu�ered" in
the tank volume, whereafter the system will equilibrate towards
Ci = C.
The concentration balance for the system are given as:
Ci ;tQ�t � CtQ�t + V (C(t+�t) � Ct) = Ci ;t � Ct +V
Q
dCt
dt
Transformed to Laplace domain.
Ci � C +V
Q(sC � C0)
By choosing to start the simulation at concentration 0 each time C0 disappears and the transfer
function can be isolated.
C =
Q
V
s +Q
V
Ci
In this case were Q kept constant at 0.36 ml/min, V is �xed as 1.26 ml, which gives an Q=V
of 0.286.
41
AU � Engineering Membrane properties
D Membrane properties
The following table contains product information on the porous PTFE membranes donated by
POREX [33].
PMV10
Water entry pressure (WEP) min 175, typical 270 mbar
Air �ow min 70, typical 125 l/hr/cm2 �p 70 mbar
Thickness 0.13 mm (nominal)
UL Rating V-0, f2 UL 94, UL746C
IP Rating 64 / 67 BS EN 60529: 1992
Filtration e�ciency 0.5 � (99.99%) IEST RP-CC007.2 2009
PMV15
Water entry pressure (WEP) min 265, typical 380 mbar
Air �ow min 45, typical 70 l/hr/cm2 �p 70 mbar
Thickness 0.18 mm (nominal)
UL Rating V-0, f1 UL 94, UL746C
IP Rating 64 / 67 / 68 BS EN 60529: 1992
Filtration e�ciency 0.4 � (99.99%) IEST RP-CC007.2 2009
BM95
Water entry pressure (WEP) min 265, typical 380 mbar
Air �ow min 45, typical 70 l/hr/cm2 �p 70 mbar
Thickness 0.18 mm (nominal)
Pore size (mean capillary �ow) 3 Microns (nominal)
BM100
Water entry pressure (WEP) min 175, typical 270 mbar
Air �ow min 70, typical 125 l/hr/cm2 �p 70 mbar
Thickness 0.13 mm (nominal)
Pore size (mean capillary �ow) 4 Microns (nominal)
42
AU � Engineering Reagent cost
E Reagent cost
The reagent cost is an estimate on bulk chemical prices over the reagent composition outlined
in the seawater method, section 6.
g/L or mL/L $/kg or $/L $/L
OPA reagent
OPA [39] 001.34 50.00 0.067
Ethanol [39] 200.00 21.00 0.200
Sum 0.267
Sul�te reagent
Sodium sul�te [39] 00.38 25.00 0.002
Boric Acid [39] 15.46 20.30 0.005
Tri-sodium citart [40] 58.82 30.00 1.765
Formaldehyde [39] 25.00 20.35 0.002
Sum 1.773
43