A F -B M

A F -B M
A FREUNDLICH-BASED MODEL FOR
PREDICTION OF PH-DEPENDENT
SULFATE ADSORPTION IN FOREST
SOIL
Muhammad Akram
August 2015
TRITA-LWR Degree Project
ISSN 1651-064X
LWR-EX-2015:22
Muhammad Akram
TRITA LWR Degree Project 15:22
©Muhammad Akram 2015
Degree Project for the master program in Environmental Engineering and
Sustainable Infrastructure
Ground water chemistry
Division of Land and Water Resources Engineering
KTH Royal Institute of Technology
SE-100 44 STOCKHOLM, Sweden
Reference should be written as: Akram, M (2015) “A Freundlich-based model
for prediction of pH-dependent sulfate adsorption in forest soil” TRITALWR Degree Project 15:22
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A Freundlich based model for prediction of sulfate adsorption in forest soil
S UMMARY IN S WEDISH
Den starka industrialiseringen i Europa efter andra världskriget medförde att
stora mängder SO2 och NOx släpptes ut i samband med förbränning av fossila
bränslen. De svenska skogsekosystemen påverkades av utsläpp av SO2 följt av
depostion av H2SO4. Detta medförde att skogsmarkens förråd av sulfat (SO42-)
ökade. Denna masteruppsats studerar adsorptionen av SO42- i podsolers Bshorisonter i svensk skogsmark. Jordprov från fem olika provtagningspunkter
studerades, och resultaten visar att jordarna förmår ackumulera varierande
mängder av adsorberat SO42- beroende på förändringar i jämviktskoncentration
och pH-värde. Den här studien visar att mängden adsorberat SO42- (mmol/kg
jord) ökar med ökande jämviktskoncentration SO42- (mmol/l) och med
sjunkande pH-värde. Detta observades i jämviktsexperiment på laboratoriet.
För att beskriva resultaten utvecklades en modell för att kunna förutsäga
förrådet adsorberat SO42- (mmol/kg) i de olika jordproverna. En
Freundlichbaserad modell användes, och mängden adsorberat SO42- (mmol/kg)
beräknades som funktion av pH och av jämviktskoncentrationen SO42(mmol/l) i marklösningen. Den utvidgade Freundlichmodellen optimerades på
tre olika sätt: (1) genom obegränsad optimering då alla tre koefficienter Kf, m
och y optimerades samtidigt, (2) genom begränsad optimering då värdet för y,
som betecknade den mängd vätejoner (H+) som bands till ytan för varje
adsorberad sulfatjon, sattes till 2, och (3) genom en förenklad
tvåpunktskalibrering, där en begränsad optimering gjordes för endast två
prover från varje jord användes för varje jord. Determinationskoefficienten R2,
samt värdena för de optimerade koefficienterna, var mycket likartade för
obegränsad och begränsad optimering, beroende på att det optimerade värdet
för y var nära 2 för 4 av 5 jordar. Värdet för R2 översteg 0,96, och 0,99 för de
två jordar (Risbergshöjden B och Kloten Bs) som hade högst kapacitet att
adsorbera sulfat. Även den förenklade tvåpunktskalibreringen gav goda
anpassningar med värden för de optimerade koefficienterna som låg nära de
som fanns när hela mängden datapunkter användes i modellkalibreringen. Den
förenklade tvåpunktskalibreringen ansågs vara den bästa optimeringsmetoden,
eftersom den endast kräver två observationer för varje jord.
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A Freundlich based model for prediction of sulfate adsorption in forest soil
S UMMARY IN E NGLISH
The industrialization in Europe after World War II released the large amounts
of SO2 and NOx during the combustion of fossil fuels. The Swedish forest
ecosystems were affected by discharges of SO2 followed by deposition of
H2SO4. This meant that the forest soil reservoir of SO42- were increased. This
master thesis study the adsorption of SO42- in podzolic Bs horizons of Swedish
forest land. The adsorption results of soil samples from five different sampling
points show that the soils are able to accumulate varying amounts of adsorbed
SO42- by depending on the change in the equilibrium concentration and pH.
This study shows that the amount of adsorbed SO42- (mmol/kg soil ) increases
with increasing equilibrium concentration of SO42- (mmol/l) and with
decreasing pH. This was observed in equilibration experiments in the
laboratory. To describe the results, developed a model to predict reservoirs of
adsorbed SO42- (mmol/kg) in the different soil samples. A Freundlich based
model was used, and the amount of adsorbed SO42- (mmol/kg) was calculated
as a function of pH and the equilibrium concentration of SO42- (mmol/l) in the
soil solution. The extended Freundlich model was optimized in three different
ways: (1) by unconstrained optimization when all three coefficients Kf , m and y
were optimized simultaneously, (2) by constrained optimization when the value
of y, which signifies the amount of hydrogen ions (H+) bound to the surface
together with each adsorbed sulfate ion, was set to 2, and (3) through a
simplified two-point calibration, where a constrained optimization was made
for only two samples from each soil. The coefficient of determination R2, and
the values of the optimized coefficients were very similar for the unconstrained
and constrained optimization, as the optimized value of y was close to 2 for 4
of 5 soils. The value of R2 exceeded 0.96, and 0.99 for the two soils
(Risbergshöjden B and Kloten Bs1) that had the highest capacity to adsorb
SO42-. The simplified two-point calibration produced the values of the
optimized coefficients that were close to those obtained when the entire
number of data points were used in the model calibration. Therefore the
simplified two-point calibration was considered the best optimization method,
since it requires only two observations for each soil.
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A Freundlich based model for prediction of sulfate adsorption in forest soil
A CKNOWLEDGEMENTS
First of all, I would like to thank my supervisor Prof. Jon Petter Gustafsson for
accepting me as a master thesis student and gave me an opportunity to work
under his guidance and supervision, apart from this fact, I got the opportunity
to work with him on this interesting thesis subject. His suggestions on literature
selection, guidance in performing experiments in the laboratory and report
writing without which it would not have been possible to accomplish this
thesis. I would also like to thank Charlotta Tiberg, a PhD student at the
Swedish University of Agricultural Sciences Uppsala who provided soil samples
and helped me by giving useful guidance and information about the soil
sampling sites. I would also like to acknowledge the support and help given by
Ann Fylkner and Bertil Nilsson during Ion Chromatography analysis and other
experimental work at the Department of Land and Water Resources
Engineering.
I would also give thank to Md. Annaduzzaman a PhD student at Division of
Land and Water resources Engineering, who has helped to format the thesis
report. He always sincerely motivated me during this whole period of thesis
work.
I would also like to deeply oblige my parents, brothers and sisters for their
continuous prayers, love and moral support.
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A Freundlich based model for prediction of sulfate adsorption in forest soil
A BBREVIATIONS AND S YMBOLS
Al
Al3+
Ca+
CaSO4·2H2O
DOC
Fe
H+
HNO3
IEAs
K+
Kf
M
MgSO4
Mg+
N
NOx
Na2SO4
NO32NH4
OHR2
SO2
SO42USDA
USEPA
WHO
y
Aluminum
Aluminum ion
Calcium ion
Calcium sulfate dihydrate (Gypsum)
Dissolved organic compound
Iron
Hydrogen ion
Nitric Acid
International environmental agreements
Potassium ion
Freundlich coefficient
Non-ideality parameter in Freundlich equation
Magnesium sulfate
Magnesium ion
Nitrogen
Nitrogen oxide
Sodium sulfate
Nitrate ion
Ammonium
Hydroxyl ion
Coefficient of determination in regression equation
Sulfur dioxide
Sulfate ion
United state department of agriculture
United state environmental protection agency
World health organization
The Proton co-adsorption stoichiometry
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A Freundlich based model for prediction of sulfate adsorption in forest soil
T ABLE OF C ONTENTS
SUMMARY IN SWEDISH ................................................................................. III
SUMMARY IN ENGLISH .................................................................................. V
ACKNOWLEDGEMENTS ............................................................................... VII
ABBREVIATIONS AND SYMBOLS ................................................................. IX
TABLE OF CONTENTS ................................................................................... XI
ABSTRACT .......................................................................................................... 1
1.
INTRODUCTION ...................................................................................... 1
2.
BACKGROUND .......................................................................................... 2
2.1. FOREST SOIL SYSTEM ..............................................................................................3
2.2. ABATEMENT IN ACID DEPOSITION ..........................................................................4
2.2.1. North America, Europe and eastern Asia ...............................................................4
2.2.2. Sweden .............................................................................................................5
2.3. ADSORPTION ..........................................................................................................5
2.3.1. Factors affecting sulfate adsorption in soils ................................................................5
2.4. MECHANISM OF SULFATE ADSORPTION...................................................................6
2.4.1. Chemistry of sulfate adsorption ..............................................................................6
2.5. BACKGROUND OF STUDY........................................................................................6
2.6. SCOPE AND OBJECTIVE ...........................................................................................8
2.6.1. Importance of study .............................................................................................8
2.6.2. Scope ................................................................................................................8
2.6.3. Objective ...........................................................................................................8
3.
MATERIALS AND METHODS ................................................................. 8
3.1. SITE AND SOIL DESCRIPTION ..................................................................................8
3.2. PHYSICAL CHARACTERISTICS OF SOIL SAMPLES........................................................9
3.2.1. Phase separation and pH measurement ..................................................................10
3.3. EXTRACTION OF INITIALLY ADSORBED SO42-........................................................10
3.3.1. Extraction of initially adsorbed SO42- by phosphate .................................................10
3.3.2. Extraction of initially adsorbed SO42- by bicarbonate ...............................................12
3.4. MEASUREMENT OF THE SOIL MOISTURE CONTENT ...............................................12
3.5. SO42- MEASUREMENT ............................................................................................12
3.5.1. Calculation of added concentration of SO42- - C added .................................................12
3.5.2. Calculation of initial concentration of SO42- present in soil- C init. .................................12
3.5.3. Calculation of dissolved concentration of SO42- - Caq .................................................13
3.5.4. Calculation of sorbed concentration of SO42- – C sorbed ...............................................13
4.
MODELING APPROACH ........................................................................ 13
4.1. THE FREUNDLICH EQUATION...............................................................................13
4.1.1. Limitations .....................................................................................................13
4.2. EXTENDED FREUNDLICH EQUATION ...................................................................13
4.3. OPTIMIZATION STRATEGY ....................................................................................15
4.3.1. Unconstrained fit ..............................................................................................15
4.3.2. Procedure of optimization ....................................................................................15
4.3.3. Constrained fit .................................................................................................16
4.3.4. Procedure of optimization ....................................................................................16
4.3.5. Simplified two-point calibration ............................................................................16
4.3.6. Procedure of optimization ....................................................................................16
5.
RESULTS AND DISCUSSION ................................................................. 17
5.1. INITIAL EXTRACTABLE SO42- PRESENT IN SOILS ....................................................17
5.2. SULFATE ADSORPTION ISOTHERMS .......................................................................19
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5.3. FITTING THE EXTENDED FREUNDLICH MODEL FOR SULFATE ADSORPTION. ........20
5.3.1. The proton co-adsorption stoichiometry - unconstrained fit ..........................................20
5.3.1. The proton co-adsorption stoichiometry - constrained fit..............................................21
5.3.2. The proton co-adsorption stoichiometry- simplified two-point calibration ........................22
5.4. DISCUSSION ..........................................................................................................23
5.5. CONCLUSION ........................................................................................................24
5.6. PRACTICAL SIGNIFICANCE OF THE MODEL ............................................................24
5.7. FUTURE RECOMMENDATION ................................................................................24
REFERENCES .................................................................................................. 25
OTHER REFERENCES ................................................................................... 27
APPENDIX I ..................................................................................................... 29
APPENDIX II .................................................................................................... 31
APPENDIX III .................................................................................................. 32
APPENDIX IV ................................................................................................... 33
APPENDIX V .................................................................................................... 33
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A Freundlich based model for prediction of sulfate adsorption in forest soil
A BSTRACT
The period of industrialization after the second World War in Europe released SO2
and NOx by combustion of fossil fuels and contributed the formation of S and N
compounds in the forest ecosystem. The Swedish forest soil systems were influenced
by emissions of SO2 followed by H2SO4 deposition, consequently the pool of SO42had increased in the forest ecosystem. This thesis studied SO42- adsorption in a
podzolic Bs horizon soils taken from a Swedish forest soil system. The soil samples
from five different sampling sites were collected and the results revealed different
amounts of adsorbed SO42- in response to changes in equilibrium concentration and
pH. This study found that the amount of adsorbed SO42- (mmol/kg) increased with an
added equilibrium concentration of SO42- (mmol/l) and with a decreasing pH. This
was determined by equilibration experiments. Based on the results a Freundlich-based
model was developed to predict the pool of adsorbed SO42- in the soil samples. The
model predicted the pool of adsorbed SO42- (mmol/kg) as a function of pH and the
equilibrium concentration of SO42- (mmol/l) in the soil solution system. The extended
Freundlich model was optimized in three different ways: by use of unconstrained,
constrained and simplified two-point calibration. The results showed that the
adsorption of sulfate in the Kloten Bs1 and Risbergshöjden B soils was higher as
compared to the Tärnsjo B, Österström B, and Risfallet B soils. The coefficient of
determination (R2) determined from an unconstrained fit of the extended Freundlich
model (with three adjustable parameters) for Risbergshöjden B and Kloten Bs1 were
R2 =0.998 and R2=0.993. Nearly as good fits were found in a constrained fit with two
adjustable parameters when it was assumed that nearly 2 protons (2 H+) are coadsorbed with one SO42- ion (Risbergshöjden B; R2=0.997 and Kloten Bs; R2=0.992).
The simplified two-point calibration with two adjustable parameters showed similar
parameter values for all most soils and was considered the best optimization method
of extended Freundlich model, especially as it requires only limited input data.
Key Words : Sulfate; Spodosols; pH Dependent Sulfate Adsorption; Extended
Freundlich Model.
1.
I NTRODUCTION
Acidic deposition which is mainly consists of sulfuric acid H2SO4, nitric
acid HNO3 and ammonium NH4+, are primarily derived from emissions
of sulfur dioxide SO2, Nitrogen oxide NO2 and ammonia NH3. These
compounds are largely emitted to the atmosphere by fossil fuel
combustion and some agriculture activities (USDA and WHO, 2000).
The fossil fuels combustion which is largely for power generation, for
industrial production process and by households, provide a significant
contribution to air pollution in urban areas and on a regional or wider
scale (Mitchel et al., 1998; van Stempvoort, 1992). These emissions lead
to acidic deposition in the form of sulfuric acid H2SO4, nitric acid HNO3
and ammonium NH4+ to ecosystems. Once acid compounds enter
sensitive ecosystems, they acidify soil and surface water by causing
several ecological changes. In sensitive ecosystems, along with the
acidification of soil and surface water, they affect nutrient cycling and
impact the ecosystem services provided by forests. The atmospheric
inputs of acidifying compounds derived from fossil fuel combustion
hence disturb the soil ecosystem (Martinson et al., 2005). The long-term
deposition of acidifying compounds on soil mainly results in three types
of changes in soil: depletion of base cations, mobilization of dissolved
inorganic aluminum and accumulation of sulfate and nitrogen
(Krauskopf et al.; 1995; Schwartz et al., 2011).
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The acidic emissions that contain compounds of sulfur (S) have
oxidation states ranging from -2 (sulfide) to +6 (sulfate) (Prietzel et al.,
2009). In the unsaturated zone of forest soils, S is present as the
dominant and stable form of inorganic sulfate. Lower oxidation-state
inorganic compounds are also present but in negligible quantities.
Concentrations of sulfate (SO42-) in soils fluctuate throughout the year.
Because of variations in the balance between atmospheric inputs,
decomposition of plants, plant uptake, leaching and microbial activity
change SO42- concentration. In forest ecosystems, inorganic SO42- exists
in the form of soluble salts and adsorbed SO42- on the surface of
inorganic components of soil (Scherer, 2001; Eriksen, 2008).
Deposition of S and nitrogen (N) has led to acidification of soils and
water in Europe. Different studies show that the soils are acidified by
deposition of acidic emissions (Sverdrup et al., 1998). Deposition of S
has however decreased substantially during the last decades and many
acidified lakes show clear signs of recovery in eastern North America
and Europe (Johnson, 1980). However, much of the problem with
acidified soils and water still remains.
A decreased atmospheric deposition has altered the ecosystem of soils.
The recovery of soil in response to decrease in deposition is delayed, a
considerable time may be needed for recovery. The release of already
adsorbed SO42- is not completed until a new steady-state, with respect to
current atmospheric inputs, is obtained. The delayed effect of SO42adsorption/desorption on the response of water systems to changes in
the input acidity hence demands an accurate model to predict the
recovery from acidification, and also to predict the delay of the soil
chemical response to acidification due to altered forest management
practices.
2.
B ACKGROUND
In forest ecosystems acid deposition occurs as wet deposition (rain and
snow), dry deposition (gases and particulates), and as cloud and fog
deposition (Fig. 1). During wet deposition nitrogen oxides (NOx) and
sulfur dioxide (SO2) are converted to nitric acid (HNO3) and sulfuric
acid (H2SO4) and deposited to the forest ecosystem. Deposition of SO42and nitrate (NO3-) by wet deposition are considered roughly equivalent
(Piirainen et al., 2002), whereas deposition of ammonium NH4+ in dry
deposition form is higher. Dry deposition of SO2 and NOx leads to the
deposition of acid after interacting with water in the forest ecosystem.
NO3- and ammonium byproducts are used by forest vegetation to
support growth.
When sulfuric acid H2SO4 is deposited from the atmosphere into the soil
system, each molecule splits into two hydrogen ions (H+) and a
negatively charged SO42- ion (Alewell et al., 1995). Soil is acidified by the
presence of H+ ion to replace base cations by ion exchange process.
Furthermore, removal of displaced base cations acidify the soil system
(Harrison et al., 1989). Moreover, SO42- is retained in the soil system. It is
retained in a variety of forms, such as adsorbed SO42- on soil particles
and as organic S. It is also leached from the soil and accompanied by an
equivalent amount of base cations (Ca+, Mg+ and K+). When SO42- is
retained by sulfate adsorption it delays the loss of base cations through
leaching with SO42- and thus counters the acidifying effect of
atmospheric sulfur S deposition (Jung et.al., 2011). Understanding the
association between the inputs of S and forest soil ecosystem chemistry
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A Freundlich based model for prediction of sulfate adsorption in forest soil
Fig.1. Emissions of sulfur dioxide SO2 and nitrogen oxide
compounds NOx into the atmosphere as a source of dry and wet
acid deposition in soil. Source: USDA Forest Service
(http://webcam.srs.fs.fed.us/pollutants/acidification)
to appraise the response of forest ecosystem to acid inputs has been
considered as critical (Mitchell et al., 1998; Barton et al., 1999).
Significant work has been done on the movement and reaction of SO42in soils. Some research has been performed to predict the adsorption of
SO42- in forest soil system. According to Gustafsson (1995) and Karltun
(1997), the adsorption of SO42- in forest soil is a proton-buffering
process. This characteristic of SO42- adsorption delays the soil water
chemical response to changes in H+ and SO42- ions concentration of the
permeating solution. This may, for example, reduce the immediate
impact of atmospherically deposited H2SO4 when the latter has been
increased. This characteristic of sulfate adsorption is considered
significant in reducing base cation losses (Gustafsson, 1995; Jung et al.,
2011; Karltun, 1997). Base cations such as Ca+ ,K+ and Mg+ leach from
the soil with SO42- as a counter-ion. As a result of adsorption, SO42- is
retained in soil together with the base cations.
2.1. Forest soil system
The forest soil is a multifaceted heterogeneous medium consisting of
solid phases that contain organic matter and different minerals (Gobran
et al., 1998; Carlsson et al.; 1999). The soils that are developed in sandy
glacial tills with low weathering rates are the most vulnerable part of the
forest ecosystem to atmospheric acidic inputs (Gustafsson and Jaks,
1993). The retention of SO42- in soils is characterized by the particle
surfaces which contribute to adsorption. Soil particles with clay minerals
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and various oxide surfaces and solid phase humic substance usually
possess large specific surface areas and reactive sites. Coarser particles
such as sand possess very low surface area and hence are not important
adsorbents (Gustafsson et al., 2007).
In humid regions the process of soil formation involves leaching of
upper layer with accumulation of material in lower layers. In coarse
textured glacial tills or sandy sediments, podzols are developed by the
process of podzolisation. When organic matter present on the surface of
soil releases abundant organic acids, the latter migrate downwards
together with weathered Fe and Al in the soil profile (David et al.; 1983;
Edwards, 1998; Alves et al., 2004; Gustafsson et al., 2007). During this
process, organic acids form complexes with weathered Fe and Al and
these are deposited in the subsoil horizon in the soil profile. In this
subsoil horizon the complexes degrade, which leads to the formation of
Fe and Al hydrous oxides.
Podzolised forest soils that contain Fe oxide and poorly crystalline
aluminosilicate in the B horizon are important for SO42- adsorption. The
surfaces of these Fe and Al hydrous oxides serve as adsorbents for SO42especially under low pH conditions. SO42- adsorption in forested soil
systems is dependent on pH, quantity of Al and Fe hydroxide, organic
matter and concentration of sulfate present in the soil system (Jung et al.,
2011). In acidic soils, SO42- is adsorbed to the surface of amorphous iron
and aluminum oxide and hydrous oxide.
SO42- in Swedish forest soils is adsorbed somewhat unevenly. The spodic
B horizon has the maximum number of positive charges ions in the form
of Fe and Al (hydr)oxides. Therefore in this horizon, and when organic
carbon is low, SO42- is adsorbed to a significant extent (Grerup et al.;
1987; Gustafsson, 1995).
2.2. Abatement in acid deposition
The abatement in acid deposition in various regions of the world as
compared to Sweden can be seen as,
2.2.1. North America, Europe and eastern Asia
The SO2 emissions have declined during the last decade in Europe and
North America due to implementation of international laws, policies and
agreements (i.e. IEAs) on the reduction of S (Finus et al., 2003), but
instead a rapid increase have been observed in areas of world which have
high economic growth such as south-east Asia (Akselsson et al., 2013).
Since 1970, the deposition level has decreased by as much as two thirds
in Europe (Akselsson et al., 2013; Martinson, 2003). Already in 1984, it
was observed that emission of SO2 and SO42- deposition had declined by
between 38 and 82 % in Europe and by 52 % in the United States
(Johnson, 1984). Additionally, emissions of NOx and nitrogen
deposition show a slighter decline of 17 to 20 %. According to the
literature, in Europe, in 1980 the SO2 emissions was recorded as 55 Mt
(million ton) but this level decreased to 41 Mt (million ton) in 1990. It is
noticed that the mean annual pH of the precipitation in eastern North
America and Europe is in the range of 3.0 to 4.7 (Chesworth, 2008;
Johnson, 1984).
On the other hand in the Asian-Pacific region emissions in 1990 reached
about 35 Mt and are expected to increase rapidly. The effect of
widespread acid deposition due to sulfur emission may have decreased in
Europe but it is highly likely to increase in the Asian developing
countries (WHO, 2000).
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A Freundlich based model for prediction of sulfate adsorption in forest soil
Acid deposition in north-east Asia has increased hastily in the past
decade because of industrial growth and will most likely exceed stages
noticed previously in the most polluted area of central and eastern
Europe (Cole et al., 1997; Zhang, 1996). Consequently, the increase in
emissions is a threat to sustainable forest ecosystems and a question of
concern to take account of reduction in emissions(Ishiguro et al.; 2011).
2.2.2. Sweden
In Sweden, the decrease in the deposition of SO42- and H+ due to the
restriction (due to implementation of Environmental Protection Act
1969) of sulfur emissions started during the 1970s. They decreased
considerably during the last decade (by following the targets of the
Helsinki protocol in 1985 to reduce S emissions, the Oslo protocol in
1994 for further reduction S emissions, and the Gothenburg protocol in
1999 to abate acidification, eutrophication and ground level ozone) and
now it is at level below that recorded in the mid-1950s. The continual
decrease of the deposition resulted in an improved status of the water
quality in forested catchments in Sweden (Fölster et al., 2002). However,
the SO42- concentration in the forest ecosystems and surface waters of
south-west of Sweden has not decreased to the extent that could be
expected from the decreased acid deposition. During the period of
deposition decrease the desorption of already adsorbed sulfate acts as a
buffering mechanism in forest soils. Depending on the soil properties,
there may be a long delay between the decreased input of acid and the
chemical recovery(Nömmik et al.;1998; Jönsson et al.; 2003).
2.3. Adsorption
SO42- and other anions such as phosphate, arsenate and molybdate
adsorb on the surface of adsorbents present in the soil. These anions are
adsorbed through a reaction between the adsorbate (anions) and the
surface of a solid adsorbent (Fe and Al oxide in soils) that involves
ligand exchange (Selim et al.; 2004; Belyazid et al.; 2006; Gustafsson et
al., 2007; Sokolova et al.; 2008).
2.3.1. Factors affecting sulfate adsorption in soils
The pH and the equilibrium concentration are two important factors that
govern the adsorption of SO42- ions. The pH value is considered to be
the most important parameter. The reason is that the surface of
adsorbent usually possesses variable charge and therefore the
electrostatic forces of attraction are also variable and depend on the pH
value. For example, SO42- is adsorbed more strongly at low pH on the
variable positively charge surfaces of Fe and Al hydrous oxides in soils.
At high pH a negative charge occurs on the surface, hence cations are
adsorbed more strongly at high pH (Rao, et al.; 1984; Sharpley, 1990;
Stanko et al.; 2008).
In certain cases, the adsorption of the ion itself affects the pH values in
the surrounding environment. When one SO42- ion is adsorbed to the
surface of Fe oxide as a surface complex, it decreases the charge of oxide
surface by a value of 2. To compensate for this large change in charge,
H+ ions and to some extent other cations are bound on the oxide surface
(Gustafsson, 2007; Karltun, 1997; Gustafsson, 1995)
The effect of ionic strength changes the number of co-adsorbed
monovalent cations during sulfate adsorption on the surface of oxide
surfaces in soil. At high ionic strength i.e. under conditions of high
salinity this value is about 1, because 1 H+ is needed to protonate the
surface for every sulfate ion being adsorbed. At low ionic strength, the
number of co-adsorbed protons is nearly equal to 2 (Gustafsson, 1995).
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2.4. Mechanism of sulfate adsorption
Sulfate is retained in the soil system by varying mechanisms. The main
adsorption mechanism is called ligand exchange. In this specific
adsorption mechanism SO42- is associated with metal (hydr) oxides of Fe
and Al present in the soil system by displacing OH- anions or H2O.
During specific adsorption, the surface also accepts or donates protons,
for the reasons stated in the above section. During the adsorption of
SO42- on Fe and Al hydrous oxide surfaces, the sulfate anion accepts a
proton from the positive site of Fe and Al hydrous oxide surface (MOH2+ where M= Fe or Al) and create monovalent HSO4-. This
monovalent ion replaces a OH- ion without creating additional negative
charge on the surface (Sjöström, 1993; Gustafsson, 1995; Zhang et al.,
1996; Karltun, 1997; van Hees et al.; 2000).
The adsorption process of sulfate removes the acidity of soil solution
and during desorption process acidity is released. Due to this, the
recovery of soil is also delayed.
2.4.1. Chemistry of sulfate adsorption
Adsorption of SO42- results in the displacement of –OH ligands from
oxide:
Oxide-SO4-+OH(1)
Oxide-OH+SO4-2
When an -OH from the metal (hydr)oxide is replaced, the surface charge
decreases, which facilitates cation exchange. In reality, the replacement
usually occurs in two steps: (i) H+ ions are sorbed, and (ii) SO42- ions
bind by replacing -OH2+. Reaction (1) may therefore more accurately be
written as follows:
Oxide-SO4-+H2O
(2)
Oxide-OH +H++ SO42The release of water changes the charge from positive to negative on the
site. These equations show that SO42- adsorption and the cation
exchange capacity may increase at the same time (Gustafsson, 1995;
Karltun, 1997; Martinson et al., 2003; Goldberg, 2005 ).
Another related way to understand SO42- adsorption is by surface
complex formation theory (Gustafsson, 1995). According to this theory,
sulfate ions adsorb onto Fe and Al hydrous oxides as outer- and innersphere complexes. The adsorption of SO42- as an inner-sphere surface
complex means that adsorption of SO42- changes the net charge on the
oxide surface. The electrostatic non-specific type of adsorption creates
outer-sphere surface complexes and it balances the positive charge
surface of the metal oxides. On the other hand, adsorption of SO42- as
inner-sphere complexes is stronger.
2.5. Background of study
This thesis takes its starting point in the modeling approaches of
Gustafsson (1993 and 1995), Karltun (1997), Martinson (2003), and
Gobran et al. (1998).
Gustafsson (1995) modeled pH-dependent sulfate adsorption in the Bs
horizons of podzolised soils. He assumed that ̴ 2 H+ ions are consumed
for every SO42- ion during adsorption. It was accomplished by sequential
leaching process with use of magnesium sulfate MgSO4. Use of acid until
pH 4.4 was reached facilitated determination of the SO42- adsorption
capacity in soils.
(3)
>MOH2(H20)n++SO42-+H+ >MOH2(H20)n+HSO422The basic adsorption reaction of SO4 (equation 3) was used to predict
how the pH dependency of SO42- adsorption can be incorporated in an
6
A Freundlich based model for prediction of sulfate adsorption in forest soil
empirical model. This was tested in a Temkin isotherm approach in
which the amount of adsorbed sulfate was assumed to be linearly related
to log-transformed values of SO42- and H+. Further it was assumed that
the soil systems had very low ionic strength so that the value of y (the
proton co-adsorption stoichiometry, i.e. the number of H+ that
accompanies every SO42- ion) is close to 2. This means that an extra H+
is adsorbed in the basic reaction and that the sulfate adsorption reaction
can be viewed as the adsorption of H2SO4. Hence in this approach, the
adsorption of sulfate ion SO42- was assumed to be linearly related to the
term 2pH + pSO4, where pSO4 is the negative log of the dissolved
sulfate concentration.
Similar studies were made by Karltun (1997), although he used a surface
complexation model approach to describe his data. He compared the
surface complexation of SO42- and H+ between goethite, gibbsite and a
soil material from a podzol B horizon. He used the diffuse layer model
and found that a model with only one SO42- surface species and no H+
ion explicitly take part in the adsorption reaction provided the best
prediction of adsorption. He found that associated H+ co-adsorption
occurs during SO42- adsorption and by this the neutralization in the inner
layer the surface potential is decreased. He also performed his
experiments under different pH, ionic strength and SO42- concentrations
to determine the y value, which was found to vary with pH and SO42concentration and with the ionic strength. His experimental work
determined the y as being close to 1 at high ionic strength (0.1 M) but at
low ionic strength (0.001 M) y was in the range of 1.5 to 1.7.
Courchesne & Hendershot (1989) measured the adsorption and
desorption of SO42- to/from some podzolic soils of the southern
Laurentians in Canada as a function of pH and used six podzolic soils
(Hermine B, Coniferous B, Laflamme 1 B1, Laflamme 1 B2, Laflamme 2
B1 and Laflamme 2 B2) of two forested watersheds of southern
Laurentians. The effect of soil solution pH on SO42- of podzolic soils
was determined. They used four simple adsorption equations i.e. the
Gunary equation, Freundlich equation, Langmiur equation and Temkin
equations and observed SO42- adsorption and desorption as a function of
pH and initial sulfate concentration. They observed an increase in SO42adsorption with decreasing pH to a maximum adsorption at pH 3.8 to
4.2. They could also relate the amount of adsorbed SO42- and total native
SO42- to the total oxalate extractable Al contents of soils. They found the
Gunary equation to produce the best fits to the soil data (R2=0.999,
R2=0.995, R2=0.993, R2=0.999, R2=0.994 and R2=0.999 respectively) of
each six soils as compared to Freundlich equation (R2=0.983, R2=0.977,
R2=0.987, R2=0.972, R2=0.980, and R2=0.948 respectively).
Martinsson et al., (2003; 2005) parameterized, evaluated and modeled the
adsorption of SO42- by an isotherm in which it was assumed that SO42adsorption is fully reversible and depends on the concentration of SO42as well as the soil solution pH. The isotherm they used was in fact an
extended Freundlich equation, which is described in detail below in
chapter 4. The adsorption model was implemented in the dynamic
multilayer soil chemistry model SAFE. The batch experimental work was
performed at different pH and SO42- concentrations. In this research the
model was evaluated by applying to the roof covered catchment at Lake
Gårdsjön in the south west of Sweden.
7
Muhammad Akram
TRITA LWR Degree Project 15:22
2.6. Scope and objective
2.6.1. Importance of study
As the increased deposition of acidic compound in soil after WW II in
Europe increased the acidity and the amount of adsorbed SO42- in forest
soil. After the implementation of S emission abatement practices, the
deposition of acidic compounds in soil is decreased. The response of
reduction in emissions and acid deposition in soil is not the same. There
is a lag of time to recover from acidity in soil. The adsorbed SO42- under
reduced acid deposition conditions will continuously release acidity (H+)
and leachable SO42- to the soil solution. This action of desorption has
delayed the soil water chemical response to changes in the H+ and SO42ion concentrations of the permeating solution.
To facilitate correct dynamic models for acidification recovery it is
important to develop a robust model for the prediction of the adsorbed
pool of SO42-. In this thesis work different experiments have been
performed to investigate the extent of adsorption in five different soil
samples from Swedish Podzols. The results of the equilibration
experiments were used to optimize the model. Ultimately, the following
questions will be answered:
1. Can the extended form of Freundlich equation predict the adsorbed
pool of SO42- in forest soil?
2. Which optimization approach is the best considering the requirement
to use as few samples as possible to bring down analysis costs?
2.6.2. Scope
This thesis presents an attempt to develop a model to predict the pool of
adsorbed SO42- in the Bs horizons of podzolic Swedish forest soils. Such
a model is of interest due to the delayed effect sulfate
adsorption/desorption has on the response of water systems to changes
in the input acidity. Hence an accurate model is needed to be able to
predict the recovery from acidification, and also to predict the delay of
the soil chemical response to acidification due to altered forest
management practices.
2.6.3. Objective
The objective of this study is therefore to calibrate a Freundlich equation
for the prediction of SO42- adsorption using experiments data in which
the adsorption of SO42- is studied as a function of pH and dissolved
equilibrium concentrations of SO42-. In the calibration, five soil samples
were selected from well-developed spodic B horizons in five different
locations from Swedish forest soils.
3.
M ATERIALS AND M ETHODS
3.1. Site and soil description
The soil samples used in the investigation were sampled from five
different locations. The four soil samples (Tärnsjö B, Risfallet B,
Risbergshöjden B and Kloten Bs1) were sampled from the Bergslagen
area which is situated west of Uppsala, and one soil (Österström B) was
from Holm, to the west of Sundsvall (Fig. 2). The samples were collected
in May and July 2012. All sampled soils are Podzols (Table 1) and the
samples were collected from the upper part of the B horizons (Bs1). The
exact sampling depth of each soil was different (Table 2) and varied
between the locations.
8
A Freundlich based model for prediction of sulfate adsorption in forest soil
Fig. 2. Map to indicate the location of sampling sites of Tärnsjö B,
Risbergshöjden B,.Kloten Bs1, Risfallet B and Österström B soils.
3.2. Physical characteristics of soil samples
The physical characteristics of soil samples were determined. The soils
varied in texture, particle size, moisture and color (Fig. 3). As these soil
samples were taken from the spodic B horizons, they had reddish-brown
color due to the presence of Fe, Al and humic substances.
The Tärnsjö B soil sample was dark brown, less moist and a little coarser
in texture. In physical appearance, the Risfallet B soil was dark and more
moist than Tärnsjö B. Risbergshöjden B and Österström B were more
fine, dark and with much moisture present in soils. The Kloten Bs1 soil
was mixed with clay and was much moist and sticky in nature.
The suspension of soil samples were prepared according to the recipe
(Appendix I) by adding 2 g of soil, then adding volume of water as per
the recipe, then adding 0.10 mM MgCl2 as background electrolyte and
lastly SO42- (using the appropriate amount of Mg2+ and H+ as counter
ions) was added at the amounts specified in the recipe. Each suspension
was prepared in duplicate. After that the lid was tightly attached to all
centrifuge bottles and placed in a rack. The rack with 40 centrifuge
bottles was inserted in the end-over-end shaker and was fixed tightly.
The rack along with bottles was shaked for 6 days to reach equilibration
at room temperature (21oC). After 6 days of shaking, the bottles were
removed from the end-over-end shaker and placed in the centrifuge for
centrifugation at 3500 rpm for 15 minutes to separate the soil and
solution phases. After centrifugation, the bottles were removed from the
centrifuge carefully to avoid phase mixing and placed at room
temperature to cool down for a while.
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Muhammad Akram
TRITA LWR Degree Project 15:22
3.2.1. Phase separation and pH measurement
The bottles were transferred to the pH meter. A Radiometer PHM 93,
Copenhagen pH meter was used. 40 scintillation bottles (20 ml) were
prepared and marked to store the filtrate of each equilibrium suspension
accordingly. The pH meter was calibrated according to standard
procedures. After this, 5 ml of the supernatant was taken by using a
Biohit pipette, transferred to the pH measurement bottle and the pH
measurement was started (the results of the pH measurements for each
series are shown in Appendix II). The remaining phase-separated
supernatant (15-20 ml) was filtered using an Acrodisc PF 32
mm0.8/0.2 µm membrane syringe filter (Pall Corp., Washington, NY,
USA) and the filtrate was transferred into a scintillation bottle marked
with the appropriate sample number.
3.3. Extraction of initially adsorbed SO42-
To be able to know the amount of adsorbed SO42- in equilibrium with a
certain dissolved SO42- concentration, the amount of adsorbed SO42- is
determined by calculating initially adsorbed SO42- and additionally
adsorbed SO42-.
For the data treatment it was required to quantify the initially adsorbed
amount of SO42- in the soil samples. This was done in two ways: by the
phosphate and by bicarbonate extraction.
3.3.1. Extraction of initially adsorbed SO42- by phosphate
For the purpose of determining initially adsorbed SO42- in soil, an initial
solution of 20 mM NaH2PO4 was prepared. Extraction of initially
adsorbed SO42- was done to all five soil samples individually. For each
soil the extractions were carried out in duplicate. For this purpose, 10
centrifuge bottles were prepared by washing with acid and deionized
water, and then dried. All centrifuge bottles were marked according to
the soil samples consequently. After this, 2 g of moist soil was added to a
centrifuge bottle. Then 20 ml of 20 mM NaH2PO4 was added. The lid
was attached to the bottle and placed into the rack. The rack was
adjusted tightly to the end-over-end shaker and shaken for 24 hours at
Table 1. General properties of Tärnsjö B, Risbergshöjden B,
Österström B, Kloten Bs1 and Risfallet B sampling sites.
Site
Land
use
Vegetation
Topography
Groundwater
table
Drainage
Risfallet
Forestry
Coniferous forest,
birch. Moss, grass
Hilly
> 80 cm
Rather
well
drained
Tärnsjö
Forestry
Coniferous forest
(pine). Moss,
lichen
Flat
> 80 cm
Well
drained
Risbergshöjden
Forestry
Coniferous forest.
Lichen,
lingon/blueberry
Hilly
> 80 cm
Well
drained
Kloten
Forestry
Coniferous forest.
Grass, heather,
moss
Slightly
sloping
> 80 cm
Well
drained
Österström
Forestry
Confierous forest.
Lichen, lingon/blue
berry
Hilly
> 80 cm
Well
drained
10
A Freundlich based model for prediction of sulfate adsorption in forest soil
Fig. 3. Images of (a) Tärnsjö B; (b) Risbergshöjden B; (c)
Österström B; (d) Kloten Bs1 and (e) Risfallet B soil samples
before equilibration experiments.
Table 2. General properties of Tärnsjö B, Risfallet B,
Risbergshöjden B, Österström B and Kloten Bs1 soils.
pH
Oxalate
-Al
Soil
Horizon
Depth (cm
below
surface)
(0.01 M
CaCl2)
(mmol /kg)
(mmol
/kg)
Tärnsjö
Bs1
2-16
4.88
45
118
Risfallet
Bs1
7-15
4.24
151
265
Risbergshöjden
Bs1
4-13
4.39
119
534
Österström
Bs1
5-15
4.13
85
166
Kloten
Bs1
14-24
4.73
114
647
11
Oxalate-Fe
Muhammad Akram
TRITA LWR Degree Project 15:22
room temperature. After shaking, bottles were removed and placed in
the centrifuge. The centrifugation was at 3500 rpm for 15 minutes. After
centrifugation bottles were removed carefully to avoid phase mixing.
After this, filtration of the extracts was done by using Acrodisc PF
32 mm 0.8/0.2 µm membrane syringe filters attached to a plastic syringe.
The filtered extract of each soil solution was stored in 20 ml scintillation
bottles.
3.3.2. Extraction of initially adsorbed SO42- by bicarbonate
For the extraction of initially adsorbed SO42- by bicarbonate, 40 mM
NaHCO3 was prepared. The same five moist soils were used to extract
initially adsorbed SO42-. The same procedural steps were followed as for
extraction by phosphate to prepare suspensions, shaking, centrifugation
and filtration.
3.4. Measurement of the soil moisture content
The results for SO42- adsorption were reported in terms of sulfate
adsorbed per gram weight of dry soil. For this reason it was required to
measure the moisture content of soil samples. The moisture content of
each soil sample was measured as follows: First the oven was set at
105oC. Five clean and dry porcelain crucibles were weighted and was
noted as the initial weight of the crucible. 3 to 5 g of soil sample was
added to the porcelain crucible and placed again on a balance, the weight
of moist soil and crucible was noted (up to 3 decimals). After this, the
crucible with soil sample was placed in the oven to dry for 24 hours.
After drying for 24 hours the crucible was removed from the oven and
was transferred carefully and immediately to an excicator to let it cool
down for 20 minutes. After this, the sample was taken out from the
excicator and weighed exactly (three decimals). This same procedure was
adopted for each soil, the results of soil moisture content are in
Appendix IV.
3.5. SO42- measurement
The filtrates stored in the scintillation bottles were analysed for SO42using ion chromatography. A Dionex DX-120 instrument (Dionex
Corp., Sunnyvale, CA, USA) was used to measure the amount of
dissolved SO42- (mg/l) for all samples from the batch equilibrations and
from the extractions.
3.5.1. Calculation of added concentration of SO42- - C added
The concentration of added SO42- was calculated by using the recipe for
each suspension preparation. However, it needed to be corrected for (a)
a slight deviation of 7 % between the nominal concentration and the
final one, as found after repeated IC analysis of the stock solution, and
(b) the amount of water present in the field-moist soil (which causes a
slight dilution). The resulting value of Cadded was expressed in µmol/l.
3.5.2. Calculation of initial concentration of SO42- present in soil- C init.
The calculation of initial concentration of SO42- present already in the
soil was done with the help of phosphate extraction. During extraction
of initial SO42- by phosphate the filtrate extract was analysed by ion
chromatography. The L/S (liquid to solid ratio) was calculated with the
help of the moisture content of each sample. The calculated L/S value
was used to calculate the experimental SO42- (mmol/kg of SO42-). After
this these values given in mmol/kg were converted to initial
concentration Cinit. of SO42- µmol/l present in the samples.
12
A Freundlich based model for prediction of sulfate adsorption in forest soil
3.5.3. Calculation of dissolved concentration of SO42- - Caq
The calculation of dissolved concentration of SO42- was done by taking
the average of SO42- dissolved (mg/l) in duplicate samples measured by
ion chromatography for each soils, divided with the average value of
dissolved SO42- (mg/l) with the molecular weight of SO42- (96.06 g/mol).
Then this value was multiplied by 1000 to obtain the units of Caq in
µmol/l.
3.5.4. Calculation of sorbed concentration of SO42- – C sorbed
The concentration of sorbed SO42- was calculated by using the values of
C init, C added and C aq. For this, first the general calculations were done by
using the relationship of these above mentioned concentrations as,
Cinit+(Cadded - Caq) µmol/l. The result obtained was in µmol/l, it was
converted to µmol/kg by multiplying L/S derived by using soil in
equilibration experiments.
4.
M ODELING APPRO ACH
4.1. The Freundlich equation
The basic Freundlich equation is the derived form of linear KD model
with adjustable parameters m and Freundlich coefficient Kf .
The general form of Freundlich equation is as:
(4)
The non linear relationship between adsorbed concentration of solute
(sulfate) Q (mol/kg) and dissolved concentration C (mol/l) gives a slope
less than 1.
4.1.1. Limitations
This simple form of Freundlich equation is useful to fit the adsorption
data only at fixed pH. In addition it cannot explain the competition of
ions.
As we are interested in simulating pH-dependent SO42- adsorption, there
is a need to extend the simple Freundlich equation. Through the
extended Freundlich equation, the major drawbacks of the simplistic
equation can be resolved.
4.2. Extended Freundlich equation
To overcome the limitations of simple Freundlich equation, it can be
extended by including extra terms of activity of H+ i.e.{H+} and
concentration of competing ions with adjustable parameters. The version
of the extended Freundlich equation to be used in this thesis can be
expressed as:
(5)
The logarithmic form of the equation can be written as
(6)
(7)
where Q represents the amount of adsorbed sulfate in mol/kg, C is the
equilibration concentration of sulfate measured in mol/l, Kf is the
Freundlich coefficient measured as the y-intercept in Freundlich
equation, and m is the slope.
E quation (7) implies that we can plot (Fig. 4) adsorbed SO42- as
log Q (mol/kg) on the y axis against dissolved SO42- as log C (mol/l) and
pH on the x axis.
13
Muhammad Akram
TRITA LWR Degree Project 15:22
Fig. 4. Freundlich equation isotherm expressing the amount of
adsorbed sulfate log Q (mol/kg) as a function of equilibrium
concentration log C (mol/l).
Fitting the extended Freundlich equation for SO42- adsorption:
During SO42- adsorption onto hydrous oxides of Fe and Al, a certain
number of H+ ions is co-adsorbed (i.e. the number of H+ ions that
accompany each SO42- ion during adsorption) to prevent excess charge
development on the surface of minerals (hydrous) oxide. Hence, we can
write the SO42- adsorption reaction as follows:
(8)
SO42- + y H+ ads-SO4
where y is the number of protons e.g. number of H+ co-adsorbed to
prevent excess charge development. It varies depending on the ionic
strength. At high ionic strength, i.e. when the salinity is high, the number
of co-adsorbed H+ needed to protonate the mineral surface for SO42- to
adsorb is close to 1. With a decrease in salt content at low ionic strength
I the number of co-adsorbed proton H+ is close to 2. We may derive the
hypothetical equilibrium constant of the above equation as:
=K
(9)
We may then express this in terms of the extended Freundlich equation,
in which the exponent m describes the non-ideality of the dissolved
components. Furthermore, the SO42- ion activity SO42-} is replaced with
the term total dissolved SO42- i.e. [SO42-]t as is customarily the case in the
Freundlich equation, and we get,
14
A Freundlich based model for prediction of sulfate adsorption in forest soil
ads-SO4 = Kf ( SO42- ]t{H+}y m
(10)
where ads-SO4 is expressed in mol/kg and represents all adsorbed SO42-.
It includes the amount of SO42- sorbed during the experiment and
initially present adsorbed SO42-.The sorbed SO42- is calculated by
subtracting the concentration of dissolved SO42- from the added
SO42(mmol/kg). Kf and m are the coefficients of the Freundlich equation
(the y intercept and slope respectively after log-log transformation). The
total dissolved sulfate SO42- ]t is expressed in mol/l.
Equation (10) can be written in the logarithmic form as:
log ads-SO4 = log Kf + m (log SO42- ]t + y log {H+})
(11)
+
as we know pH = -log{H }
log ads-SO4 = log Kf + m (log SO42- ]t – y(pH))
(12)
2The plot of log ads-SO4 on the y axis against log SO4 ]t – y.(pH) on the
x axis should provide a straight line according to the extended
Freundlich equation, after adjustment of the value of y to an optimum
value. In practice during the calculations, the trendline tool in the
Microsoft Excel was used to provide the best fit using linear regression.
For the unconstrained fit (section 4.4.2), a trial-and-error method was
used to simultaneously arrive at optimum values of y, Kf and m.
4.3. Optimization strategy
The optimization of extended Freundlich equation (12) was done in
three different ways:
• Unconstrained fit. In this method, the values of y, Kf and m were
optimized simultaneously without any constraints on their values.
• Constrained fit. A constant value of y was assumed, which means that
only Kf and m were optimized.
• Simplified two-point calibration. This method also used a constant value
of y, but only two data points with different pH and [SO42-]t were
used in the optimization.
During optimization, the data of each soil was processed individually.
4.3.1. Unconstrained fit
By definition, the unconstrained fit function is the fit of data by means
of all three adjustable parameters y, Kf and m. To optimize the extended
Freundlich equation (Equation 12) the unconstrained fit requires a wide
range of pH values and dissolved sulfate concentrations to be successful,
because otherwise different combinations of y, Kf and m can equally well
describe the data.
4.3.2. Procedure of optimization
During optimization the following procedural steps were adopted,
• Calculation of the term log SO42-]t (mol/l) from the data set for each
individual soil.
• Calculation of log ads-SO4 (mol/kg).
• The use of relationship log SO42-]t – y(pH).
• Optimization of the value of y by the trial-and-error method.
• log ads-SO4 was plotted as a function of log SO42-]t – y(pH).
• The trendline (linear) tool was used to produce the regression
equation and R2 values (five decimal points).
• The value of y was again optimized by the trial-and-error method to
obtain a new value of R2, and the steps above were repeated until the
optimum combination of y and R2 values were found.
15
Muhammad Akram
TRITA LWR Degree Project 15:22
• At this point the values of the slope (m) and the y-intercept (log Kf)
were collected from the graph.
• The Freundlich coefficient Kf was calculated from log Kf.
4.3.3. Constrained fit
In the constrained fit the adjustable parameter y is selected as common
value of 2. The value of 2 was chosen because it was thought to
represent low-ionic-strength conditions as found in the forest soils
acceptably well (Background section). The constrained fit has the
advantage that optimization of only two parameters results in more
robust estimates and thus it does not require such a large variation in pH
and dissolved sulfate concentrations.
4.3.4. Procedure of optimization
During optimization following procedural steps were adopted,
• Calculation of the term log SO42- ]t (mol/l) from the data set for
each individual soil.
• Calculation of the term log ads-SO4 (mol/kg).
• The relationship of log SO42- ]t – 2pH was used.
• log ads-SO4 was plotted as a function of log SO42- ]t – 2pH.
• The trendline (linear) tool was used to produce the regression
equation and R2 values.
• The slope m and the y intercept log Kf were taken from the regression
equation.
• The Freundlich coefficient Kf was calculated from log Kf.
4.3.5. Simplified two-point calibration
In the simplified two-point calibration only two data points were selected
from the data set and used in the optimization. By this method it was
tested whether it was possible to select only two points from the data set
and still be able to produce a reliable model. By using the simplified twopoint calibration, the use of the extended Freundlich model will be much
easier, because large sets of soils can be optimized with a limited number
of observations.
4.3.6. Procedure of optimization
• From each soil data set, the duplicate samples according to the recipe
with 0.1 mM MgCl2 only were selected. For example, for Tärnsjö B,
sample A1 and A2, for Risbergshöjden B, sample B1 and B2, for
Österström B, sample C1 and C2, for Risfallet B, sample A27 and
A28, and for soil Kloten Bs1, sample D1 and D2 were selected
(Appendix V), and the average value of each duplicate sample were
calculated.
• Selection of the pH value of each respective soil samples and
calculation of average of each duplicate pH value.
• Similarly, selection of the dissolved sulfate value SO42- ]t (mmol/l)
and adsorbed sulfate values (mmol/kg) for each respective soil
samples and calculation of the average and log of each duplicate
dissolved sulfate and adsorbed sulfate values.
• In the same manner, the duplicate sample with the addition of highest
amount of SA solution according to the recipe (resulting in 0.05 mM
MgSO4 + 0.05 mM H2SO4) was used, since these samples differed
significantly in both pH and dissolved sulfate compared to the
0.10 mM MgCl2 samples. For example, for Tärnsjö B, sample A25
and A26, for Risbergshöjden B, sample B25 and B26, for Österström
16
A Freundlich based model for prediction of sulfate adsorption in forest soil
•
•
•
•
•
•
•
5.
B, sample C25 and C26, for Risfallet B, sample A39 and A40, and for
Kloten Bs1, sample D25 and D26 from the data set were selected
(Appendix V) , and the average of each sample values were
calculated.
Again the average of pH values for each respective sample of highest
SA solution were calculated.
The dissolved SO42- value SO42- ]t (mol/l) and adsorbed SO42(mol/kg) for each respective soil samples were selected and the
average and the logs of each duplicate dissolved SO42- and adsorbed
SO42- were calculated.
The term log SO42- ]t – 2pH was used.
A graph between log SO42- ]t – 2pH on the x axis vs log ads-SO4 on
the y axis was plotted.
The trendline (linear) tool was used to the data of each soil to display
the regression equation and R2.
The values of the slope m and the y intercept log Kf were taken from
regression equation.
The Freundlich coefficient Kf was calculated from log Kf.
R ESULTS AND D ISCUSSION
Firstly, in this section the initially extractable adsorbed SO42- present in
each soil samples and correlation between initially adsorbed SO42- with
the amount of Fe and Al hydrous oxide as determined by oxalate
extraction can be expressed as,
5.1. Initial extractable SO42- present in soils
The initially adsorbed SO42- present in the soils extracted by phosphate
extraction is different in each soil. It may depend on the location of the
sampling sites, depth, soil type, the nature of sampling site, and the type
of forest ecosystem (Table 2). The initially adsorbed SO42- (Fig. 5)
present in the soil samples extracted by phosphate (sodium phosphate,
NaH2PO4) shows that the extracted amount of SO42- in Risbergshöjden
B soil is high (4.55 mmol/kg) as compared to other soils. The second
largest amount of SO42- initially adsorbed is in Kloten Bs1,
4.17 mmol/kg. Similarly, in Risfallet B, Tärnsjö B and Österström B,
initially adsorbed SO42- extracted by NaH2PO4 is 1.30 mmol/kg,
0.78 mmol/kg and 0.61 mmol/kg respectively.
The high value of initially bound sulfate in Risbergshöjden B and Kloten
Bs1 is well correlated (Fig. 6) with the amount of Fe and Al hydrous
oxide as determined by oxalate extraction. The high amount of oxalate
extractable Fe in Kloten Bs1 (114 mmol/kg) and oxalate extractable Al
(647 mmol/kg) and in Risbergshöjden B (119 mmol/kg and
534 mmol/kg Fe and Al respectively) as compared to other soil provide
evidence (Fig. 6) that Risbergshöjden B and Kloten Bs1 soils have high
value of initially bound sulfate.
17
Muhammad Akram
TRITA LWR Degree Project 15:22
Fig. 5. The amount of initially adsorbed SO42- (mmol/kg) in the
Tärnsjö B, Risbergshöjden B, Österström B, Kloten Bs1, and
Risfallet B soils.
Fig. 6.Plot to represent the effect of oxalate extractable Fe and Al
on initially adsorbed SO4218
A Freundlich based model for prediction of sulfate adsorption in forest soil
5.2. Sulfate adsorption isotherms
The sulfate adsorption isotherms (Fig. 7) of Tärnsjö B, Risbergshöjden
B, Österström B, Kloten Bs1, and Risfallet B soils used in the study were
determined by plotting the equilibrium concentration of sulfate (mmol/l)
against the amount of SO42- adsorbed (mmol/kg) in soil. Comparing the
highest amount of SO42- adsorbed (mmol/kg) in each soil, it is evident
that the soils differ in terms of their SO42- adsorption capacity. The
results for adsorption of SO42- (Table 3) show that the maximum
concentration of SO42- adsorbed in Tärnsjö B soil is 3.93 mmol/kg when
the pH was 4.71 and the dissolved SO42- concentration was
0.348 mmol/l.
The soil data plotted in Fig. 7 are the mean values of duplicate samples.
The pattern of SO42- adsorption as a function of equilibrium
concentration for all levels of sulfate addition is the same for all soils.
Fig. 7. Adsorbed SO42- (mmol/kg) during the experiment as a
function of equilibrium concentration of SO42- (mmol/l) for (a)
Tärnsjö B; (b) Risbergshöjden B; (c) Österström B; (d) Kloten
Bs1; (e) Risfallet B.
Table 3. Amount of adsorbed SO42- after addition of 0.5 mM SO42-.
Soil
Tärnsjö B
Risbergshöjden B
Österström B
Kloten Bs1
Risfallet B
Maximum SO42- adsorbed
(mmol/kg)
3.93
8.25
2.29
9.26
1.83
19
pH at maximum SO42adsorption
4.71
4.45
4.22
4.65
4.82
Muhammad Akram
TRITA LWR Degree Project 15:22
The values for adsorbed SO42- include the initial sulfate adsorbed in each
soil. The difference in the amounts of adsorbed SO42- in each soil is well
correlated with the amount of sulfate that was initially adsorbed, and
maximum adsorbed SO42- with oxalate-extractable Fe+Al (Fig. 6). It is
evident from Fig. 6 that SO42- adsorption increased with the increase in
the concentration of SO42-, but also that the equilibrium pH had a strong
effect on the result. There is illustrated that the amount of sulfate
adsorbed (mmol/kg) is increasing with the increase in amount of sulfate
in equilibrium solution at any given equilibrium pH value.
The trends of the isotherm of each soil (Fig. 7) explain the concept of
adsorption of SO42-. The general tendency of an increase in sulfate
adsorption with a decrease in pH is understandable. At low pH, the soils
possess more positive surface charge. The different sulfate adsorption
behavior of different soils can be attributed partly to differences in
competitive adsorption of other anions and organic compounds in the
soil.
5.3. Fitting the extended Freundlich model for sulfate adsorption.
The fitting of the extended Freundlich model for SO42- adsorption can
be expressed by Unconstrained, Constrained and Simplified Two point
fits as;
5.3.1. The proton co-adsorption stoichiometry - unconstrained fit
When the sorption data for all five soils sample were plotted between log
SO42- ]t – y(pH) on the x axis and log ads-SO4 on y axis by using
unconstrained fit Freundlich equation (Fig. 8), it showed that the
adsorption data were well described for all soils. The co-adsorbed
number of proton y during SO42- adsorption in each soil (Table 4) was
different but ideally it should be close to 2, because of the low ionic
strength in these systems.
From Fig. 8 it seems that the extended Freundlich model showed an
excellent fit to the data particularly at lower concentration.
From the unconstrained fit (Table 4) it seems that Risbergshöjden B and
Fig. 8. Unconstrained fits of extended Freundlich model for
Tärnsjö B, Risbergshöjden B, Österström B, Kloten Bs1, and
Risfallet B soil samples.
20
A Freundlich based model for prediction of sulfate adsorption in forest soil
Table 4. Co-adsorbed stoichiometry (y), Coefficient of
determination (R 2), slope (m), and Freundlich coefficient (Kf) for
soil samples – unconstrained fit.
Soil
y
Equation
m
log Kf
Kf
R2
Tärnsjö B
1.98
y = 0.2364x + 0.6467
0.236
0.646
4.425
0.975
Risbergshöjden B
2.44
y = 0.1385x – 0.0926
0.138
-0.092
0.809
0.995
Österström
B
3.85
y= 0.1493x + 0.2856
0.149
0.285
1.927
0.986
Kloten B
2.05
y = 0.1753x + 0.251
0.175
0.251
1.782
0.993
Risfallet B
2.20
y = 0.1078x – 1.2318
0.107
-1.231
0.058
0.982
Kloten Bs1 showed the best fit (y= 2.44, R2= 0.995, and y=2.05, R2 =
0.993 respectively) followed by Österström B, Risfallet B and Tärnsjö B.
5.3.1. The proton co-adsorption stoichiometry - constrained fit
In the constrained fit y is set to 2, and hence Fig. 9 was constructed with
log SO42- ]t – 2(pH) on the x axis and log ads SO4 on the y axis. In the
constrained fit of the extended Freundlich model Risbergshöjden B
showed the best fit (m= 0.148 and R2=0.997). The values of the slope m,
the coefficient of determination R2 and the y-intercept log Kf are shown
in Table 5.
Fig. 9. Constrained fits of extended Freundlich model for Tärnsjö
B, Risbergshöjden B, Österström B, Kloten Bs1, and Risfallet B
soil samples.
21
Muhammad Akram
TRITA LWR Degree Project 15:22
Table 5. Co-adsorbed stoichiometry (y), Coefficient of
determination (R 2), slope (m), and Freundlich coefficient (Kf) for
soil samples – Constrained fit.
Soil
y
Equation
m
log Kf
Kf
R2
Tärnsjö B
2
y = 0.2354x + 0.6577
0.235
0.658
4.54
0.975
Risbergshöjden B
2
y = 0.1483x – 0.2518
0.148
-0.252
0.56
0.997
Österström
2
y= 0.1944x – 0.3888
0.194
-0.389
0.41
0.964
Kloten B
2
y = 0.1786x + 0.2244
0.177
0.224
1.67
0.993
Risfallet B
2
y = 0.1091x – 1.3192
0.109
-1.319
0.04
0.982
5.3.2. The proton co-adsorption stoichiometry- simplified two-point calibration
The simplified two-point calibration is in fact a simplified version of the
constrained fit, where only two data points were selected. The plot of log
SO42- ]t – 2pH on the x axis and log ads-SO4 on the y axis (Fig. 9) gives
the extended Freundlich model parameters (Table 6) for Tärnsjö B,
Risbergshöjden B, Österstrom B, Kloten Bs1 and Risfallet B soil.
To get R2 values that were comparable to those obtained for the other
fits, the R2 values shown in Table 6 are those obtained when using the
optimized coefficients for the whole data set (not just the two data
Fig. 10. Plot between predicted amount of adsorbed sulfate (log C
sorbed, mol/kg) and observed amount of adsorbed sulfate (log
Kf+m([log SO42- ] t– y(pH )) for Tärnsjö B, Risbergshöjden B,
Österström B, Kloten Bs1 and Risfallet B soil.
22
A Freundlich based model for prediction of sulfate adsorption in forest soil
Table 6. Co-adsorbed stoichiometry (y), Coefficient of
determination (R 2), slope (m), and Freundlich coefficient (Kf)
for soil samples – two-point calibration
Soil
y
Equation
m
log Kf
Kf
R2
Tärnsjö B
2
y = 0.3844x + 3.0087
0.384
3.009
1018
0.975
Risbergshöjden B
2
y = 0.1523x – 0.1991
0.152
-0.199
0.63
0.997
Österströ
mB
2
y= 0.2032x – 0.2442
0.203
-0.244
0.57
0.964
Kloten B
2
y = 0.1855x + 0.3419
0.186
0.342
2.20
0.992
Risfallet
B
2
y = 0.1082x – 1.3376
0.108
-1.338
0.045
0.982
points used during calibration). The simplified two-point calibration with
two adjustable parameters of the extended Freundlich model of each soil
data set (Table 6) shows that each soil data set has a similar coefficient of
determination R2 as obtained by the constrained fit (Table 5). This shows
that the two-point calibration method resulted in surprisingly good fits
despite the small number of data points used.
5.4. Discussion
The results obtained by modeling the data set of all five soils show that
the optimization strategy of the extended Freundlich model in three
different ways i.e. unconstrained, constrained and simplified two-point
calibration is promising. The unconstrained fit of the extended version
of Freundlich model gives an y value of close to 2 for Risbergshöjden B
and Kloten Bs1 soil data set; it supports the presumption that y = 2 at
low ionic strength I. It also validates the assumption that the
unconstrained fit of extended Freundlich model is virtually equal to that
of the constrained fit model (e.g. for Kloten Bs1, R2 =0.993 and R2=
0.992 by using unconstrained and constrained fit at y = 1.98 and y = 2,
respectively). By this, it is validated that the assumption of common
stoichiometry y = 2 is the optimum value to calibrate the model by using
different soil data sets. It implies that it is advantageous to optimize only
two parameters m and Kf of the extended Freundlich equation to
calibrate the soil data set. Consequently, the real power of the
constrained fit is proved, it allows us to calibrate the model with much
less data available. Moreover, the optimization using the simplified two
point calibration procedure shows results that are usually in close
agreement with those of the constrained fit (e.g. for Kloten Bs1 by using
constrained fit and simplified two-point fit it obtained m=0.177 and
m=0.186, Kf=1.6 and Kf=2.19 respectively). However, a slight variation in
optimization parameters values were observed especially in case of the
Tärnsjö B and Österström B soil data. The reason for this is not known
at present. Due to the selection of only two points, it has a significant
advantage over the unconstrained and constrained fits, i.e. it is more
suitable to measure only pH and dissolved sulfate concentration for two
points when there are large soil data sets available to calibrate. These
benefits show the suitability to use simplified two-point extended
Freundlich model calibration.
When comparing the simplified two-point calibration of the extended
Freundlich model with the modeling approach used by Martinsson et al.
(2003), the latter authors calibrated the isotherms at a co-adsorbed
proton stoichiometry y= 1.7 by using three variables m, n and q.
However, a more robust calibration method is to optimize only two
variables (m and Kf) instead of three variables, since this leads to a better
23
Muhammad Akram
TRITA LWR Degree Project 15:22
constrained model when limited data are available. Hence, the extended
version of Freundlich model by use of the simplified two-point
calibration at y= 2 is more appropriate to use for large sets of soil data.
5.5. Conclusion
The extended Freundlich model proposed in this study is a promising
tool for predicting SO42- adsorption in soils that adsorb and desorb SO42The simplified two-point optimization strategy is the best option when
using the extended version of Freundlich model for soil data. The
suggested model is less complex and needs a smaller number of
optimized parameters (only m and Kf) compared to earlier attempts. Still,
the model is able to predict pH-dependent adsorption effects. Moreover,
all extended Freundlich model calculations and fitting is executed within
a simple Microsoft Excel worksheet, since it does not need any advanced
numerical geochemical tool.
5.6. Practical significance of the model
Practically, the extended form of Freundlich model is of great
significance to estimate the adsorption of sulfate under different
amounts of atmospheric sulfate input to the soil system, because it is
estimated that nearly 2 H+ are accompanied for every SO42- ion during
adsorption and desorption. This form of model is able to predict the
amount of adsorbed SO42- at associated equilibrium concentration of
sulfate and pH. It is especially well adapted for use in dynamic soil
chemistry models, where large amounts of soil data are needed for
predictions on a regional or national basis.
5.7. Future recommendation
The present study did not explicitly incorporate the competitive reaction
of other anions (e.g. P) and dissolved organic carbon (DOC) during
SO42- adsorption, although it may be argued that competition is indirectly
accounted for with the adjustable parameters Kf and m. The absence of
any direct account for competition effects may be a weakness in longterm scenarios in which the levels of competitors (i.e. DOC and P,
phosphate) are subject to change. In future development it is
recommended to acknowledge the influential presence of DOC and
other competitors that may play a decisive role in the mobility of sulfate
in the soil profile and may act as a negatively charged ion. This may be
done by using, e.g, more mechanistically based surface complexation
models.
24
A Freundlich based model for prediction of sulfate adsorption in forest soil
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28
A Freundlich based model for prediction of sulfate adsorption in forest soil
A PPENDIX I
Initial solution and recipes of equilibration experiments used in Series A to
Series D for all five soil samples.
Initial solutions used in sample preparation for equilibration experiments.
Initial solution
C
E
S
SA
A
SL
SAL
AL
Strength
0.01 M MgCl2
0.01 M Ca(OH)2
0.01 M MgSO4
0.005 M MgSO4 + 0.005 M H2SO4
0.01 M H2SO4
1 mM MgSO4
0.5 mM MgSO4 + 0.5 mM H2SO4
1 mM H2SO4
Recipe of Series A to D for soil Tärnsjö B Risbergshöjden B, Österström B,
Kloten Bs1 and Risfallet B for equilibration experiments.
Series A. Tärnsjö B and Risfallet B soils.
2 g of Tärnsjö B
Sample
No.
Solution C
(ml)
1,2
0.32
3,4
0.32
5,6
0.32
7,8
0.32
9,10
0.32
11,12
0.32
13,14
0.32
15,16
0.32
17,18
0.32
19,20
0.32
21.22
0.32
23,24
0.32
25,26
0.32
2 g of Risfallet B
27,28
0.32
29.30
0.32
31,32
0.32
33.34
0.32
35,36
0.32
37,38
0.32
39,40
0.32
H2O (ml)
Solution
S (ml)
Solution
SA (ml)
Solution
A (ml)
Solution
SL (ml)
Sol. SAL(ml)
31.68
30.88
30.08
31.36
31.04
30.72
30.08
30.88
30.08
31.36
31.04
30.72
30.08
0.32
0.64
0.96
1.6
-
0.32
0.64
0.96
1.6
-
0.8
1.6
-
0.8
1.6
-
31.68
30.88
30.08
31.36
31.04
30.72
30.08
0.32
0.64
0.96
1.6
-
-
0.8
1.6
-
-
Series B. Risbergshöjden B and Tärnsjö B soils.
2 g of Risbergshöjden B
Sample
No.
Solution
C (ml)
H2O
(ml)
Solution S
(ml)
Solution
SA (ml)
Solution
A (ml)
Sol. SL
(ml)
1,2
3,4
5,6
7,8
9,10
11,12
13,14
15,16
17,18
19,20
21.22
23,24
25,26
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
31.68
30.88
30.08
31.36
31.04
30.72
30.08
30.88
30.08
31.36
31.04
30.72
30.08
0.32
0.64
0.96
1.6
-
0.32
0.64
0.96
1.6
-
0.8
1.6
-
29
Sol.
SAL(m
l)
0.8
1.6
-
Sol
Al (ml)
-
Muhammad Akram
TRITA LWR Degree Project 15:22
2 g of Tärnsjö B
27,28
0.32
29.30
0.32
31,32
0.32
33.34
0.32
35,36
0.32
37,38
0.32
39,40
0.32
31.68
30.88
30.08
28.48
31.04
30.72
30.08
0.32
0.48
0.8
0.32
0.48
0.8
-
1.6
-
1.6
-
0.8
1.6
-
Series C Österström B and Risbergshöjden B soils
2 g of Österström B
Sample
No.
Sol.
C (ml)
H2O
(ml)
Sol. S
(ml)
Solution
SA (ml)
Solution
A (ml)
Sol.
SL
(ml)
Solution
SAL(ml)
Solution
Al (ml)
1,2
3,4
5,6
7,8
9,10
11,12
13,14
15,16
17,18
19,20
21.22
23,24
25,26
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
31.68
30.88
30.08
31.36
31.04
30.72
30.08
30.88
30.08
31.36
31.04
30.72
30.08
0.32
0.64
0.96
1.6
-
0.32
0.64
0.96
1.6
-
0.8
1.6
-
0.8
1.6
-
-
2 g of Risbergshöjden B
27,28
29.30
31,32
33.34
35,36
37,38
39,40
0.32
0.32
0.32
0.32
0.32
0.32
0.32
31.68
30.88
30.08
28.48
31.04
30.72
30.08
0.32
0.48
0.8
0.32
0.48
0.8
-
1.6
-
1.6
-
0.8
1.6
-
Series D Kloten Bs1
2 g of Kloten Bs1
Sample
No.
Sol.
C (ml)
H2O
(ml)
Solution
S (ml)
Solution
SA (ml)
Sol.
A (ml)
Solution
SL (ml)
1,2
3,4
5,6
7,8
9,10
11,12
13,14
15,16
17,18
19,20
21.22
23,24
25,26
27,28
29.30
31,32
33.34
35,36
37,38
39,40
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
0.32
31.68
30.88
30.08
31.36
31.04
30.72
30.08
30.88
30.08
31.36
31.04
30.72
30.08
31.68
30.88
30.08
28.48
31.04
30.72
30.08
0.32
0.64
0.96
1.6
0.32
0.48
0.8
0.32
0.64
0.96
1.6
0.32
0.48
0.8
-
0.8
1.6
1.6
-
30
Sol.
SAL(m
l)
0.8
1.6
1.6
-
Solution
Al (ml)
0.8
1.6
-
A Freundlich based model for prediction of sulfate adsorption in forest soil
A PPENDIX II
pH of filtrates of Tärnsjö B, Risbergshöjden B, Österström B, Kloten Bs1 and
Risfallet B soil solutions of series A to series D.
pH of series A
Sample
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
pH
5.39
5.37
5.54
5.57
5.62
5.58
5.67
5.67
5.64
5.62
pH of Series B
Sample
A11
A12
A13
A14
A15
A16
A17
A18
A19
A20
pH
5.61
5.63
5.67
5.59
5.50
5.54
5.43
5.43
5.30
5.34
Sample
A21
A22
A23
A24
A25
A26
A27
A28
A29
A30
pH
4.96
4.97
4.92
4.92
4.97
4.93
4.88
4.89
4.81
4.83
B31
B32
B33
B34
B35
B36
B37
B38
B39
B40
5.24
5.32
5.56
5.49
5.43
5.44
5.36
5.40
5.25
5.14
4.80
4.77
4.84
4.84
4.87
4.87
4.91
4.91
4.93
4.92
B11
B12
B13
B14
B15
B16
B17
B18
B19
B20
4.92
4.94
4.92
4.96
4.80
4.83
4.80
4.79
4.77
4.75
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
4.70
4.77
4.75
4.76
4.74
4.76
4.74
4.75
4.69
4.70
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
4.67
4.66
4.60
4.60
4.74
4.74
4.70
4.69
4.58
4.58
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
4.46
4.44
4.35
4.33
4.23
4.20
4.76
4.75
4.69
4.69
C31
C32
C33
C34
C35
C36
C37
C38
C39
C40
4.62
4.60
4.83
4.81
4.80
4.82
4.76
4.78
4.69
4.71
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
5,0
5,0
5,12
5,12
5,16
5,18
5,22
5,24
5,28
5,29
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20
5,30
5,30
5,28
5,30
5,05
5,04
5,02
5,02
4,99
4,99
D21
D22
D23
D24
D25
D26
D27
D28
D29
D30
4,90
4,90
4,81
4,83
4,66
4,64
5,03
5,05
4,98
4,98
D31
D32
D33
D34
D35
D36
D37
D38
D39
D40
4.88
4.89
5.31
5.13
5.12
5.10
5.04
5.03
4.96
4.96
pH of Series D
31
4.67
4.66
4.58
4.60
4.45
4.46
5.42
5.50
5.30
5.42
Sample
A31
A32
A33
A34
A35
A36
A37
A38
A39
A40
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
pH of Series C
B21
B22
B23
B24
B25
B26
B27
B28
B29
B30
pH
5.10
5.17
4.98
4.97
4.69
4.72
4.96
4.95
4.96
4.97
Muhammad Akram
TRITA LWR Degree Project 15:22
A PPENDIX III Ion Chromatography analysis of Tärnsjö B, Risbergshöjden B,
Österström B, Kloten Bs1 and Risfallet B soils in series A to series D.
Ion Chromatograpgy Analysis results for Series A
Sample
SO4 (mg/l)
Sample
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
0,4824
0,5119
2,1819
1,9593
4,1173
4,0318
8,3005
8,1304
17,3200
17,4019
A11
A12
A13
A14
A15
A16
A17
A18
A19
A20
SO4
(mg/l)
27,523
28,124
47,326
47,151
1,8441
1,9131
3,0533
2,8766
6,1914
6,3531
Sample
SO4 (mg/l)
Sample
SO4 (mg/l)
A21
A22
A23
A24
A25
A26
A27
A28
A29
A30
12,8805
12,6341
19,4974
19,7911
33,6371
33,2406
0,8400
0,8601
2,5523
2,5989
A31
A32
A33
A34
A35
A36
A37
A38
A39
A40
4,8192
5,1699
8,9878
9,1106
18,8844
19,1119
28,2092
28,7212
48,0948
48,3500
B31
B32
B33
B34
B35
B36
B37
B38
B39
B40
2,2224
2,3123
7,0091
7,1072
14,9442
14,8316
23,6275
23,3206
39,7426
39,7890
Ion Chromatography Analysis results for Series B
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
1,7949
1,7094
2,9815
3,1459
4,6900
4,8127
8,5925
8,4165
16,3643
16,4147
B11
B12
B13
B14
B15
B16
B17
B18
B19
B20
25,639
24,926
42,848
43,569
2,7028
2,7677
3,9983
3,9202
6,7762
6,7242
B21
B22
B23
B24
B25
B26
B27
B28
B29
B30
12,4622
12,6516
18,5641
18,3497
32,2453
33,0855
0,4999
0,6288
1,2075
1,3250
Ion Chromatography Analysis results for Series C
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
0,4
0,3
2,0
2,0
4,0
4,0
8,4
8,7
17,3
18,1
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
27,9
28,1
47,4
47,8
2,0
2,0
3,8
3,8
7,8
7,8
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
15,8
16,0
24,5
25,0
42,4
43,0
0,4
0,4
1,8
1,8
C31
C32
C33
C34
C35
C36
C37
C38
C39
C40
3,5
3,5
7,4139
7,3918
14,9385
14,4841
22,4471
22,9183
38,5700
38,9223
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
1,2922
1,2479
2,7775
2,7357
4,4895
4,5257
8,4509
8,5112
16,6165
16,5428
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20
25,9129
25,9296
43,8206
44,2471
2,2590
2,1976
3,3721
3,4284
5,9318
5,8599
D21
D22
D23
D24
D25
D26
D27
D28
D29
D30
11,6995
11,3612
17,5536
17,2820
30,1737
30,2145
1,2537
1,2911
1,9956
1,8897
D31
D32
D33
D34
D35
D36
D37
D38
D39
D40
2,3722
2,4351
7,3478
7,2789
15,2239
14,5075
22,5430
21,8371
37,2191
37,8992
Ion Chromatography Analysis results for Series D
32
A Freundlich based model for prediction of sulfate adsorption in forest soil
A PPENDIX IV Moisture content of Tärnsjö B, Risbergshöjden B,
Österström B, Kloten Bs1 and Risfallet soils.
No
1
2
3
4
5
Soil Sample
Tärnsjo B
Risfallet B
Risbergshöjden B
Österström B
Kloten Bs1
Moisture %age
5.54 %
21.46 %
17.38 %
18.78 %
32.69 %
A PPENDIX V Data used to calibrate extended Freundlich model for
Tärnsjö B, Risbergshöjden B, Österström B, Kloten Bs1 and Risfallet B soils
for Calculation of Cadded (µmol/l), Caq (mmol/l), and Csorbed (mmol/kg).
Tärnsjö B
Sample
No
Cadded
(µm/l)
Caq µmol/l
A1,A2
0
A3,A4
Caq mmol/l
Cad-Caq
Cinit+(Cad- Csorbed
Caq)
µmol/kg
Csorbed
mmol/kg
5.175535076 0.005176
5.17553508
40.77365
693.0312451 0.693031
26.65836
21.55523968 0.021555
5.1031222
51.05231
867.7379507 0.867738
A5,A6
53.31672
42.41623391 0.042416
10.9004899
56.84968
966.2760161 0.966276
A7,A8
106.6334
85.52431702 0.085524
21.1091305
67.05832
1139.792647 1.139793
A9,A10
213.2669
180.7299666 0.18073
32.5369284
78.48612
1334.031336 1.334031
A11,A12 319.9003
289.6518724 0.289652
30.2484701
76.19766
1295.134329 1.295134
A13,A14 533.1672
491.76892
0.491769
41.3983176
87.34751
1484.648686 1.484649
A15,A16 26.65836
19.55632883 0.019556
7.10203305
53.05122
901.7135098 0.901714
A17,A18 53.31672
30.86556984 0.030866
22.4511539
68.40034
1162.603067 1.162603
A19,A20 106.6334
65.29511284 0.065295
41.3383347
87.28752
1483.629154 1.483629
A21,A22 213.2669
132.8052718 0.132805
80.4616232
126.4108
2148.609089 2.148609
A23,A24 319.9003
204.4998763 0.2045
115.400466
161.3497
2742.465855 2.742466
A25,A26 533.1672
348.1036983 0.348104
185.063539
231.0127
3926.5316
3.926532
B27,B28 0
5.87508606
0.005875
5.87508606
40.0741
681.140952
0.681141
B29,B30 25.66179
13.18233073 0.013182
12.4794569
58.42865
993.1137751 0.993114
B31,B32 51.32358
23.60326902 0.023603
27.7203062
73.66949
1252.163036 1.252163
B33,B34 106.6334
73.47651358 0.073477
33.1569339
79.10612
1344.569593 1.34457
B35,B36 213.2669
154.985652
0.154986
58.2812431
104.2304
1771.608374 1.771608
B37,B38 319.9003
244.3686931 0.244369
75.5316494
121.4808
2064.814148 2.064814
B39,B40 533.1672
413.9684774 0.413968
119.19876
165.1479
2807.025593 2.807026
Risbergshöjden B
Sample
Cad
umol/l
Caq
umol/l
Caq
mmol/l
Cad-Caq
Cinit+(CadCaq)
Csorbed
µmol/kg
B1,B2
0
18,24
0,018
-18,24
214,22
B3,B4
26,46
31,89
0,032
-5,431
227,03
4444,44
4,444
B5,B6
52,93
49,46
0,049
3,46
235,93
4618,56
4,619
249,78
4889,75
4,89
5355,0
5,35
4193,69
Csorbed
mmol/kg
4,194
B7,B8
105,85
88,53
0,09
17,32
B9,B10
211,7
170,62
0,171
41,1
B11,B12
317,55
263,2
0,26
54,35
286,8
5614,7
5,62
B13,B14
529,25
449,82
0,45
79,44
311,91
6105,85
6,11
B15,B16
26,46
28,47
0,028
-2,012
230,45
4511,37
4,51
273,55
33
Muhammad Akram
TRITA LWR Degree Project 15:22
B17,B18
52,93
41,22
0,04
11,71
244,17
4779,97
4,78
B19,B20
105,86
70,27
0,071
35,58
268,04
5247,27
5,25
B21,B22
211,70
130,72
0,130
80,98
313,44
6136,06
6,14
B23,B24
317,55
192,14
0,192
125,4
357,88
7005,83
7,01
B25,B26
529,25
340,1
0,340
189,2
421,66
8254,54
8,25
C27,C28
0
4,4
0,005
-4,4
228,07
4464,71
4,46
C29,C30
25,47
18,7
0,019
6,79
239,25
4683,71
4,68
C31,C32
50,95
36,8
0,037
14,2
246,66
4828,57
4,82
C33,C34
105,85
77,06
0,077
28,8
261,25
5114,27
5,11
C35,C36
211,7
153,15
0,15
58,55
291,01
5697,0
5,697
C37,C38
317,55
236,13
0,24
81,4204
313,9
6144,66
6,145
C39,C40
529,25
403,35
0,4034
125,9
358,36
7015,34
7,0153
Österström B.
Sample
No
Cadd
umol/l
Caq
umol/l
Caq
Cinit+(Cadmmol/l Cad-Caq Caq)
Csorbed µmol/kg
Csorbed mmol/kg
C1,C2
0
3,643
0,00
-3,643
26,823
534,594288
0,534594288
C3,C4
26,44
20,802
0,02
5,638
36,103
719,5679415
0,719567942
C5,C6
52,88
41,843
0,04
11,037
41,502
827,1687951
0,827168795
C7,C8
105,8
89,177
0,09
16,583
47,048
937,7122406
0,937712241
C9,C10
211,5
184,37
0,18
27,146
57,612
1148,244394
1,148244394
C11,C12 318,0
291,38
0,29
26,640
57,105
1138,148319
1,138148319
C13,C14 528,8
495,45
0,49
33,356
63,821
1272,005677
1,272005677
C15,C16 26,44
20,83
0,02
5,614
36,079
719,0859706
0,719085971
C17,C18 52,88
39,3
0,04
13,579
44,044
877,8255999
0,8778256
C19,C20 105,8
81,02
0,08
24,736
55,201
1100,196242
1,100196242
C21,C22 211,5
165,4
0,16
46,160
76,625
1527,196579
1,527196579
C23,C24 317,3
257,7
0,25
59,627
90,092
1795,605277
1,795605277
C25,C26 528,8
444,5
0,44
84,299
114,764
2287,348673
2,287348673
Kloten Bs 1.
Sample No
C add umol/l C aq umol/l
C aq mmol/l
Cadded- Cinit+(Cad
Caq
ded-Caq)
Csorbed
µmol/kg
Csorbed
mmol/kg
D1,D2
0
13,22
0,013
-13,22
158,6
3847,9
3,848
D3,D4
26,21
28,7
0,0287
-2,483
169,37
4108,4
4,11
D5,D6
52,429
46,92
0,047
5,504
177,36
4302,09
4,30
D7,D8
104,86
88,29
0,088
16,57
188,42
4570,5
4,570
D9,D10
209,713
172,59
0,173
37,118
208,97
5068,9
5,069
D11,D12
314,6
269,84
0,267
44,727
216,58
5253,5
5,25
D13,D14
524,3
458,39
0,458
65,89
237,74
5766,7
5,767
D15,D16
26,21
23,197
0,02319
3,0171
174,87
4241,8
4,2418
D17,D18
52,43
35,397
0,036
17,031
188,89
4581,7
4,5817
D19,D20
104,86
61,38
0,061
43,48
215,34
5223,25
5,22
D21,S22
209,71
120,03
0,1200
89,68
261,54
6343,91
6,344
D23,D24
314,570
181,322
0,1813
133,25
305,11
7400,7
7,401
D25,D26
524,3
314,33
0,31
209,96
381,82
9261,42
9,261
D27,D28
0
13,25
0,02
-13,246
158,61
3847,28
3,847
34
A Freundlich based model for prediction of sulfate adsorption in forest soil
D29,D30
25,23
20,22
0,020
5,0112
176,87
4290,14
4,29
D31,D32
50,469
25,02
0,026
25,45
197,3
4785,80
4,786
D33,D34
104,86
76,13
0,076
28,725
200,58
4865,31
4,865
D35,D36
209,72
154,75
0,155
54,96
226,82
5501,7
5,50169
D37,D38
314,571
231,0
0,23
83,57
255,42
6195,7
6,196
D39,D40
524,28
390,99
0,39
133,29
305,14
7401,7
7,40166
Risfallet B
C aq umol/l
C aq mmol/l
C added - Cinit+(CaddedC aq
Caq)
Csorbed
µmol/kg
Csorbed
mmol/kg
A27,A28 0
8,95
0,009
-8,9540
53,6751
1108,12
1,108
A29,A30 26,4
26,81
0,027
-0,4165
62,2125
1284,38
1,284
A31,A32 52,8
51,99
0,052
0,7981
63,4272
1309,45
1,309
A33,A34 105,6
94,204
0,094
11,3800
74,0090
1527,92
1,527
A35,A36 211,2
197,77
0,198
13,3941
76,0232
1569,49
1,569
A37,A38 316,8
296,32
0,296
20,4247
83,0538
1714,65
1,714
A39,A40 527,92
502,00
0,502
25,9167
88,5457
1828,03
1,828
Sample
Cadded
35
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