• No results found

Flow pattern analysis of a Surface Flow Constructed Wetland: Treating surface runoff and landfill leachate water from the Löt waste management site

N/A
N/A
Protected

Academic year: 2021

Share "Flow pattern analysis of a Surface Flow Constructed Wetland: Treating surface runoff and landfill leachate water from the Löt waste management site"

Copied!
76
0
0

Loading.... (view fulltext now)

Full text

(1)

IN THE FIELD OF TECHNOLOGY

DEGREE PROJECT

TECHNOLOGY AND LEARNING

AND THE MAIN FIELD OF STUDY

ENVIRONMENTAL ENGINEERING,

SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2020

Flow pattern analysis of a

Surface Flow Constructed

Wetland

Treating surface runoff and landfill leachate

water from the Löt waste management site

(2)

Flow pattern analysis of a

Surface Flow Constructed

Wetland

Treating surface runoff and landfill leachate

water from the Löt waste management site

Max-Bernhard Alm

Supervisor

Agniezska Renman

Gunno Renman

Examiner

Bo Olofsson

Supervisor at Söderhalls Renhållningsverk (SÖRAB)

Johanna Leback

Degree Project in Environmental Engineering and Sustainable Infrastructure KTH Royal Institute of Technology

School of Architecture and Built Environment

Department of Sustainable Development, Environmental Science and Engineering SE-100 44 Stockholm, Sweden

(3)
(4)

Sammanfattning

Avfallshanterings- och återvinningsföretaget Söderhalls Renhållningsverk AB (SÖRAB) har anlagt en våtmark vid Löts avfallsanläggning, ca 35 km norr om Stockholm. Våtmarken utgör det näst sista reningssteget i reningsprocessen av lak- och processvatten från avfallsanläggningen. Riktvärdena för utsläppshalterna överskrids inte men det är önskvärt för SÖRAB att åstadkomma så låga utsläppsvärden som möjligt för att minimera påverkan på känsliga områden och vattendrag nedströms. SÖRAB misstänker dock att preferentiella flödesvägar kan förekomma där vattnet passerar alltför fort genom våtmarken. Detta resulterar ofta i en lägre reningseffektivitet då föroreningarna som är lösta i vattnet får en kortare kontakttid med de naturliga

reningsmekanismerna som förekommer i våtmarken. Syftet med det här arbetet var därför att undersöka strömningen i våtmarken och identifiera vattnets flödesvägar med hjälp av en numerisk modell utvecklad av Wörman och Kjellin (2020).

Strömningen i våtmarker styrs av en energigradient där flödet går från en punkt i ett vattendrag med högt energiinnehåll till en punkt med lågt energiinnehåll. Enligt principen om energins bevarande omvandlas energin mellan kinetisk, potentiell, tryckenergi och värmeenergi. Ändringen i energiinnehåll beror i sin tur på verkan av externa krafter (gravitationskraften, hydrostatiska tryckkrafter, friktionskrafter, kontraktions- och expansionskrafter och skjuvkrafter från vind. Dessa krafter verkar vid förändringar i bottentopografin, vattendjupet, ytmotståndet (vid våtmarkens botten och väggar), våtmarkens geometri samt där vattenytan är exponerad för vind. Dessa faktorer orsakar utvecklandet av skjuvkrafter i flödet som i sin tur orsakar utvecklandet av hastighetsprofiler och omblandning. Bildandet av hastighetsprofiler och omblandning av vattnet gör att olika

vätskeelement eller föroreningar stannar i våtmarken olika lång tid då de rör sig olika fort. För att åstadkomma en så hög reningsgrad som möjligt är det därför önskvärt att hela våtmarkens volym nyttjas till samma grad och att samtliga vätskeelement rör sig med samma hastighet genom våtmarken vilket även kallas för en ideal flödesregim (där ingen omblandning i flödesriktningen förekommer).

Då utvecklandet av skjuvkrafter i flödet utgör den grundläggande orsaken till avvikelser från en ideal flödesregim är det önskvärt att minimera dessa. De styrande faktorerna som orsakade utvecklandet av skjuvkrafter i flödet var som nämndes ovan: variationer i våtmarkens

bottentopografi och vattendjup, våtmarkens geometri (som kan orsaka isolerade vattenvolymer), ytmotståndet (som bl.a. beror på distributionen av vegetation), vind, samt in- och

utflödeshastigeter.

Våtmarken undersöktes genom inmätning och lodning som sedan låg till grund för en konceptuell modell av systemet. Den konceptuella modellen utgjorde sedan en grund för att modellera

våtmarken numeriskt. I den konceptuella modellen ingick identifiering och definition av systemgränser samt randvillkor, att definiera bottentopografin samt att dela in våtmarken i delområden med homogent flödesmotstånd. Systemgränser och randvillkor identifierades baserat på en vattenbalans. Med hjälp av vattenbalansen kunde relevanta komponenter att inkludera som randvillkor identifieras. Randvillkorens värden bestämdes genom mätningar av den hydrauliska potentialen med hjälp av en GNSS-mottagare (där GNSS står för Global Navigation Satellite System och mottagaren nyttjar satelliter för att bestämma höjd och position i en geografisk punkt) samt från erhållna mätvärden från SÖRAB av in- och utflöden som pumpas in och ut ur våtmarken. Då bottentopografin var okänd bestämdes den genom att vattendjupet mättes, interpolerades och subtraherades från en referensnivå. Vattendjupet mättes genom lodning och mätpunkterna

interpolerades sedan i det geografiska informationsverktyget ArcMap för att erhålla ett heltäckande lager av mätvärden över vattendjupet. Därefter kunde vattendjupet subtraheras från vattenytans medelhöjd över havet vilket var 38,1 m och ett heltäckande lager över bottentopografin kunde erhållas. Flödesmotståndet beräknades enligt ekvation 16 (se avsnitt 2.1.) och våtmarken delades in i homogena delområden baserat på förekomsten av vegetation och om strömningen skedde genom ett poröst medium eller öppet vatten.

(5)

Den numeriska modelleringen genomfördes genom att först modellera den nuvarande strömningen med och utan ett rör som går genom den genomsläppliga vallen. Därefter ändrades de styrande faktorerna för flödet en i taget för att kunna utvärdera vilken effekt varje faktor hade på

strömningen i våtmarken för att åstadkomma en ideal flödesregim. Följande simuleringar genomfördes: (1) Bottentopografin gjordes jämn med ett vattendjup på 0,5 respektive 1,0 m, (2) inloppszonen gjordes längre för att undvika skapandet av isolerade vattenvolymer längs

ytterkanterna, (3) vegetationens distribution gjordes homogen, (4) den genomsläppliga vallen justerades. Pålitligheten i resultatet från den numeriska modelleringen är osäker. Därför skulle ett spårämnesförsök behöva genomföras för att undersöka huruvida resultatet från modelleringen är tillförlitligt eller inte.

Enligt modelleringsresultatet förekom en tydlig flödesväg som passerade genom den smalare delen av vallen. Modelleringen indikerade vidare att de kontrollerande faktorerna som styrde flödet i våtmarken framförallt utgjordes av distributionen av vegetation samt den genomsläppliga vallen tillsammans med omgivande bottentopografi.

Det rekommenderas därför att modelleringsresultatets validitet först undersöks med ett spårämnesförsök innan några åtgärder vidtas. Möjliga förbättringsåtgärder som skulle kunna införas därefter för att sträva mot ett idealt flöde skulle kunna vara att justera den genomsläppliga vallen till att ha en lika stor tjocklek och ett lika stort djup överallt samt att justera bottentopografin runt vallen så att den förändras lika mycket runt vallen. Detta för att skapa förutsättningar för att undvika preferentiella flödesvägar genom den. En jämn fördelning av vegetation (och justering av vattendjupet till att understiga 1,5 m som tillåter kolonisering av växter) att störningar i flödet minimeras.

(6)

Abstract

The waste management and recycling company, Söderhalls Renhållningsverk (SÖRAB) have constructed a surface flow wetland in order to treat surface runoff from the waste management site, Löt. The contaminated water passes several treatment steps until it reaches the wetland and a subsequent soil infiltration step. It is suspected that the flow path of the water through the wetland is short-circuited which may result in a reduced treatment efficiency. The current discharge concentrations of the chemical compounds tested for do not exceed the allowed discharge limits. However, it is of interest to keep the discharge concentrations as low as possible to protect sensitive areas and water bodies downstream. The aim of the thesis was therefore to investigate the flow pattern of the wetland and suggest measures which potentially could improve the treatment efficiency. The flow pattern was modelled numerically in a Physio-Mathematical model developed by Wörman and Kjellin (2020). The current flow pattern was modelled, followed by several simulation runs where the controlling factors of the flow were changed one by one. The validity of the modelling result is uncertain and should therefore be confirmed or rejected by conducting a tracer test prior to implementing any changes in the wetland design. The modelling results indicate the presence of a main flow path passing through the narrower section of the permeable embankment (intersecting the northern and southern part of the wetland, see Fig. 3). The results further indicate that the permeable embankment, the bottom topography and the vegetation distribution were the three major factors controlling the flow pattern within the wetland.

Recommended improvements would therefore be to first conduct a tracer test to make sure that any changes implemented are based on the true current flow pattern. The embankment and the vegetation distribution seem to be the main causes of non-idealities in the flow but at the same time probably also have positive effects on the treatment efficiency (since they provide filtration and surface areas where microorganisms can attach to perform their treatment). One solution to reduce the non-idealities in the flow could therefore be to adjust the embankment to be equally wide and deep across the wetland. Furthermore, the bottom topography around the embankment could be adjusted so that the shift in bottom elevation is equal around it. This would probably aid in hindering the development of preferential flow paths through the embankment. Finally, the vegetation distribution could be made uniform. (It should also be noted that a uniform vegetation distribution would require adjustment of the water depth to be below 1,5 m to allow an equal establishment of vegetation).

Keywords

(7)
(8)

Acknowledgements

I would like to thank my former teachers and supervisors Agniezska Renman and Gunno Renman, my former teacher and examiner Bo Olofsson, my former teacher Robert Earon and Anders Wörman for being inspiring teachers and the people that you are. Thank you for the help in writing this thesis and with support concerning equipment needed and questions regarding the numerical model. A big thank you also, to all of the teachers at the SEED department at KTH.

I would further like to thank my supervisor Johanna Leback at SÖRAB who made this thesis possible and for your help with advice and all the practical details in investigating the wetland.

(9)
(10)

Table of contents

Introduction ... 1

Aim and objectives ... 2

Background ... 3

Description of study area ... 3

Hydraulic theory of wetlands ... 6

The hydrodynamics of wetlands ... 10

Treatment mechanisms and hydrodynamics ... 12

Materials and Methods ... 16

Conceptual model ... 16

Numerical model ... 24

Hydraulic residence time ... 30

Theoretical ... 30 Observed ... 30 Hydraulic efficiency ... 30 Results ... 31 Conceptual model ... 31 Numerical modelling ... 37

Current flow pattern ...38

Improving the hydrodynamics of the Löt wetland ... 40

Hydraulic residence time ... 49

Theoretical ... 49

Observed ... 49

Hydraulic efficiency ... 49

Discussion ... 50

(11)
(12)
(13)

1. Introduction

A wetland can be defined as a body of water which can be found either near or at the ground surface during the whole or part of the year (USEPA, 2018b, Naturvårdsverket, 2019). Wetlands are

commonly found in the transition zone between aquatic and terrestrial ecosystems (USEPA, 2008). Thereby, they may provide a range of ecosystem services such as supporting groundwater recharge, protecting the soil from drought, decreasing the risk of flooding, supporting biodiversity (both aquatic and terrestrial species), decreasing eutrophication by trapping nutrients from e.g. agricultural land and decreasing the effects of climate change (due to carbon assimilation and storage) (Naturvårdsverket, 2019). Wetlands can exist in many different environmental settings and can be characterized by the underlaying soil type, vegetation present, the hydrology of the area, water chemistry, geomorphic setting and climatological factors (USEPA, 2018a, Gunnarson and Löfroth, 2009). Wetlands exist naturally but may also be constructed to fulfil a specific purpose (Stefanakis et al., 2014a).

Constructed wetlands (CWs) may be designed to e.g. control floods, to restore wildlife habitats or to treat wastewater (Stefanakis et al., 2014a). The design may vary and CWs are therefore classified based on (1) the presence or absence of a free water surface, (2) the plant type present (i.e. free-floating plants, free-floating leaved plants, emergent or submerged plants) and (3) the prevailing flow direction. The two main categories are Surface flow wetlands (SFW) which have a free water surface and Subsurface flow wetlands (SSFW) which do not (Stefanakis et al., 2014a).

The general purpose of wetlands designed for the treatment of wastewater is to improve the water quality of the effluent water using natural treatment processes (Haberl et al., 2003). These processes, which may be physical or chemical, are provided by the soil, vegetation and associated microorganisms (Vymazal et al., 1998).

The treatment efficiency is usually correlated with a longer hydraulic residence time (HRT) (Kjellin et al., 2007). The residence time of the water is in turn affected by the flow pattern. Water parcels or contaminants found in areas with faster water movement get in less contact with the removal mechanisms or get a shorter reaction time which ultimately results in lower removal of the

contaminant (Kjellin et al., 2007). This phenomenon can be described as short-circuiting, in which the contaminants to be treated spend less time than intended in the wetland which may result in only partial or no treatment of the contaminant at all (Lightbody et al., 2008).

The waste management and recycling company Söderhalls Renhållningsverk AB (SÖRAB) have constructed a surface flow wetland to treat contaminated water originating from the waste

management site, Löt (located 35 km north of Stockholm). The wetland constitutes one of the final steps in the water treatment process prior to discharge (SÖRAB, 2019). However, it is suspected that the travel path of the water through the wetland is short-circuited and that the treatment efficiency therefore may be reduced. None of the effluent concentrations of the substances tested for exceeds the allowed discharge limits (compare Table 8 and 9 in Appendix I). However, it is desirable to achieve as low effluent concentrations as possible in order to protect sensitive areas downstream and to minimize any negative environmental impact. Maintaining a treatment efficiency of the wetland which is as high as possible is therefore of interest.

(14)

1.1 Aim and objectives

The aim of the thesis is to investigate the flow pattern of the Löt wetland with the use of a numerical model and suggest potential solutions to improve it in order to obtain a higher treatment efficiency. The aim will be fulfilled by the following objectives:

(1) To derive the physical factors that govern the flow pattern (i.e. the hydrodynamics) of wetlands based on hydraulic theory.

(2) To determine how the treatment efficiency is related to the hydrodynamics of wetlands. (3) To determine the flow pattern of the wetland by use of a numerical model.

(4) To determine whether or not the wetland is short-circuited by comparing the theoretical and observed hydraulic residence time.

(5) To suggest potential measures that could improve the flow pattern of the wetland in order to obtain a higher treatment efficiency.

(15)

1.2 Background

1.1.1. Description of study area

The waste management and recycling company, Söderhalls Renhållninsverk AB (SÖRAB), is a regional company owned by 10 municipalities located in the northern part of the Stockholm region in Sweden. The waste management site is located in Vallentuna municipality, 35 km north of Stockholm along the highway E18 (Stråe et al., 2014, SÖRAB, 2018).

The wetland at the Löt waste management site is part of a larger water treatment system which treats surface runoff and leachate water from the site. The waste management facility is mainly used for storage and treatment of contaminated soils, oil sludge and construction debris. Landfills have also been constructed for storage of contaminated soils, ashes and asbestos (see Fig. 1 and 2) (SÖRAB, 2019). The surface runoff and leachate water produced from the storage area and waste piles is collected and treated in the dams L1 (aeration and sedimentation), L4 (storage and sedimentation), L17 (storage) and the KBR (continuous biological treatment for reduction of nutrient concentrations) before it is introduced into the wetland and the following soil infiltration step (see Fig. 2) (SÖRAB, 2019).

(16)

After passing the soil infiltration step, the water is discharged into an agricultural ditch (point L3) (see Fig. 1) (SÖRAB, 2019). The ditch connects to a stream which passes the two lakes, Jälnan and Rö. Finally, the water drains to the larger stream, Norrtäljeån, and the Baltic Sea. The main purpose of the constructed wetland is therefore to act as a final barrier and polishing step of the treated water before it is discharged from the water treatment system.

Figure 2: Overview of the water treatment system at the Löt waste management site. The water collected from the site passes the dams KBR, L17, L1 and L4 prior to reaching the wetland. The wetland is hence the next to last treatment step in the process followed by soil infiltration. The arrow indicates the flow direction of the water (SÖRAB, 2019).

The wetland itself has a surface area which extends to approximately 2,3 ha. It was constructed on natural soil which was previously woodland. Within the wetland, the water depth varies between 0,05 and 1,57 m and reed beds have been established along the shallower sides and parts (see Fig. 3). Other vegetation within the wetland include sporadic tree stumps and stems that have a sparse distribution.

Permeable and impermeable embankments have been constructed within the wetland and along parts of the outer boundary. The permeable embankment was constructed within the wetland to allow water to pass from the northern to the southern part (see Fig. 3). Impermeable embankments have been constructed along the northern, southern and south western borders. The embankment along the northern border was constructed to prevent inflow of surface runoff from the forest. This water is collected at a well and diverted via a culvert to the outlet zone. The southern and south eastern border embankments were constructed to prevent the water from escaping due to low elevation.

The inlet zone is located along the northern border (marked in yellow). Water is pumped from the dams L1, L4 and the KBR and is distributed via a perforated pipe along the length of the border. The outlet zone is located along the south border (also marked in yellow) and is pumped across the

(17)

impermeable embankment and distributed across the infiltration zone. In the infiltration zone, water is allowed to infiltrate into the soil, using it as a natural filter. Finally, the treated water is discharged at point L3.

Figure 3: The Löt wetland with system borders marked in blue. The inlet zone is located to the north (yellow) and the outlet zone is located to the south (also yellow) (Google Maps, 2020).

(18)

1.1.2. Hydraulic theory of wetlands

The field of fluid mechanics forms the theoretical basis of fluid flow (or fluid dynamics). Hydraulics, part of fluid mechanics, is concerned with the practical applications of fluids in motion (Britannica, 2019). The theoretical basis of fluid dynamics is formed by three fundamental physical principles: (1) The principle of conservation of mass, (2) the principle of conservation of momentum, and (3) the principle of conservation of energy. These principles can be formulated mathematically as the equation of (1) Continuity, (2) Momentum, and (3) Energy (Anderson, 2009).

To allow the application of physical laws (normally applied on discrete mass) to a continuum fluid, the concept of the finite control volume and Reynolds Transport Theorem needs to be introduced (Anderson, 2009, Chow, 1988). A finite control volume defines a finite region of a fluid flow, a fluid element, which is defined more specifically by a control volume, V, and a control surface, S (which is perpendicular to the flow direction). The control volume may be regarded as moving with the fluid flow or to be fixed in space with a fluid flowing continuously through it (Anderson, 2009).

The flow of a fluid flowing continuously through a control volume can be described with Reynolds Transport Theorem (RTT) (see equation 1). RTT relates the time rate of change of an extensive property (values depend on the unit mass present) in a fluid (which can be either mass, energy or momentum) to the external causes producing that change. The time rate of change of an extensive property (B) can be divided into two components: (1) The time rate of change of the extensive property stored within the control volume and (2) the net outflow of the extensive property across the control surface (Chow, 1988):

𝑑𝐵 𝑑𝑡 =

d

dt∭ 𝛽𝜌𝑑∀ + ∬ 𝛽𝜌𝕍𝑑𝔸𝐶𝑉 𝐶𝑆 (1)

The flow in wetlands can be described as open channel flow (Kjellin et al., 2007). Open channel flow can be classified based on if the flow varies in space and/or time or not (Chow, 1959). The variability (or non-variability) of the flow with respect to time and space will influence the form of the

equations of continuity, momentum and energy (Chow, 1988). Therefore, the classification of open channel flow needs to be introduced.

Open channel hydraulics

Open channel flow can occur in natural watercourses such as streams and rivers or in man-made channels or pipes (which have a free water surface in contact with the atmosphere) (Chow, 1988). It can be classified with respect to how the flow depth changes with time and throughout space (Chow, 1959).

With respect to time, the flow can be classified as steady or unsteady. In steady flow, the flow depth does not change with time (or can be considered to be constant within a time interval). For unsteady flow however, the flow depth does change with time (Chow, 1959).

With respect to space, the flow can be classified as uniform or varied. For uniform flow, the flow depth does not change in space (i.e. along the channel length) and for varied flow, the flow depth changes in space. Varied flow can further be classified as gradually or rapidly varied. For gradually varied flow, the flow depth does not change significantly along the channel length. However, for rapidly varied flow, abrupt changes in flow depth may occur along the channel (Chow, 1959). Generally, since wetlands are found in low-energy environments, i.e. areas with low flow velocities and a flat landscape where there are small changes in elevation, the open channel flow in wetlands

(19)

can be assumed to be classified as steady and gradually varied (USEPA, 2008, Wörman and Kjellin, 2020).

The flow can further be classified based on the effects of viscosity of a fluid and gravity relative to the inertial forces of the flow (Chow, 1959). The flow can therefore be defined as laminar, turbulent, or transitional depending on the effect of viscosity relative to inertia. In laminar flow, the viscosity of the fluid is large compared to the inertial forces acting on the fluid which results in a smooth flow with water parcels moving along defined streamlines. For turbulent flow, the viscosity of the fluid is small compared to the inertial forces of the flow. In the case of turbulent flow, the flow paths of the water parcels are irregular and torrential. In between these two states, there is transitional flow, which is a mix of laminar and turbulent flow (Chow, 1959). The effect of viscosity relative to inertia, i.e. if the flow is laminar, turbulent or transitional can be determined with the Reynolds number (see equation 2): 𝑅𝑒 =𝑉∗𝐿 𝜐 (2) 𝑉 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑜𝑤 [𝐿 𝑇 ] 𝐿 = 𝑡ℎ𝑒 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑙𝑒𝑛𝑔𝑡ℎ [𝐿] 𝜐 = 𝑘𝑖𝑛𝑒𝑚𝑡𝑎𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 (Chow, 1959).

The effect of gravity relative to inertia can be characterized as the ratio of inertial forces to gravity forces. The flow can therefore be characterized as subcritical, critical or supercritical. In subcritical flow, the magnitude of the gravity forces is larger than that of the inertial forces. Subcritical flow has typically a low flow velocity and can be described as tranquil. In supercritical flow however, the magnitude of the inertial forces is larger than the gravity forces. The result is a rapid and exuberant flow. The Froude number is defined according to equation 3:

𝐹 = 𝑉

√𝑔𝐷 (3)

Subcritical flow: 𝐼𝑓 𝐹 < 1 → 𝑉 < √𝑔𝐷 Critical flow: 𝐼𝑓 𝐹 = 1 → 𝑉 = √𝑔𝐷 Supercritical flow: 𝐼𝑓 𝐹 > 1 → 𝑉 > √𝑔𝐷

where V is mean velocity of the flow, g is the acceleration of gravity and D is the hydraulic depth (assumed equal to the characteristic length, L, in open channel hydraulics). The hydraulic depth is defined as the cross-sectional area of the water normal to the direction of flow in the channel over the width of the free water surface (Chow, 1959).

As can be seen in the Reynolds and Froude number, the flow velocity is a major factor governing whether the flow is laminar, turbulent or transitional as well as if the flow regime is subcritical, critical or supercritical. Flow velocities are in general low in wetlands and the flow regime can therefore be expected to be laminar and subcritical (USEPA, 2008).

(20)

The Principle of Conservation of Mass

The principle of conservation of mass, states that mass can neither be created nor destroyed (Sterner, 2011). The principle can be applied to a volume of fluid and expressed as the integral equation of continuity (Chow, 1988). The extensive property is 𝐵 = 𝑚 (𝑚𝑎𝑠𝑠). Thereby, the intensive property 𝛽 =𝑑𝑚

𝑑𝑚= 1. By law of conservation of mass, 𝑑𝐵 𝑑𝑡 =

𝑑𝑚

𝑑𝑡 = 0, since mass is neither created nor destroyed. Substitution into RTT yields the basic integral equation of continuity for an unsteady, variable density flow (see equation 4):

0 =d

dt∭ 𝜌𝑑∀ + ∬ 𝜌𝕍𝑑𝔸𝐶𝑉 𝐶𝑆 (4)

For a steady, non-variable density flow, the continuity equation reduces to equation 5:

∬ 𝕍𝑑𝔸 = 0𝐶𝑆 (5)

Implying that the inflow is equal to the outflow.

The Principle of Momentum

The momentum of a fluid is a property that causes it to resist changes in velocity and direction and is equal to the mass of the fluid times its flow velocity (Akan, 2006). Hence, unless external forces such as frictional, pressure or gravity forces would act on the fluid, it would move with constant velocity and in a straight line (USEPA, 2008). The momentum equation is defined by Newton’s second law of motion which states that the sum of the forces applied on a fluid is equal to the momentum stored within the control volume and the net outflow of momentum across the control surface (Chow, 1988). If the extensive property 𝐵 = 𝑚𝕍 (𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚), the intensive property 𝛽 = 𝑑(𝑚𝕍)

𝑑𝑚 = 𝕍. The integral equation of momentum for unsteady, nonuniform (varied) flow can be defined according to equation 6:

∑𝔽 = 𝑑

𝑑𝑡∭ 𝕍𝐶𝑉 𝜌𝑑∀ + ∬ 𝕍𝜌𝕍𝑑𝔸𝐶𝑆 (6)

For a steady, nonuniform or varied flow the momentum equation reduces to equation 7:

∑𝔽 = ∬ 𝕍𝜌𝕍𝑑𝔸𝐶𝑆 (7)

The forces acting on a fluid element can be divided into body forces and surface forces. Body forces act on the fluid element at a distance, e.g. gravity. Surface forces act on the surface of the fluid element, e.g. friction and pressure forces (Anderson, 2009). In an open channel, there are in general five forces acting on a fluid element which include the force of gravity (𝔽𝑔), friction along the bottom and sides of the control volume (𝔽𝑓), contraction and expansion forces due to abrupt changes in channel cross sectional geometry (𝔽𝑒), wind shear force on the water surface (𝔽𝑤) and unbalanced hydrostatic pressure forces (𝔽𝑃 ) (for a gradually varied flow, a hydrostatic pressure distribution may be assumed) (see equation 8):

∑𝔽 = 𝔽𝑔+ 𝔽𝑓+ 𝔽𝑒+ 𝔽𝑤+ 𝔽𝑃 (8) (Chow, 1988, Chow, 1959).

(21)

The Principle of Conservation of Energy

The principle of conservation of energy or the first law of thermodynamics states that: The time rate of change of energy inside a fluid element is equal to the net flux of heat into the element plus the rate of work done by body and surface forces on the fluid element (Anderson, 2009).

In an open channel, the total energy of a fluid element, in a point (A), along a streamline above a reference datum, is equal to the sum of the kinetic head ( 𝑉𝐴2

2𝑔), pressure head (𝑑𝐴 cos 𝜃), and potential head (𝑧𝐴) (see equation 9):

𝐻 = 𝑧𝐴+ 𝑑𝐴 cos 𝜃 +𝑉𝐴

2

2𝑔 (9)

(Chow, 1959).

By the principle of conservation of energy, energy can neither be created nor destroyed, only transformed between different forms (Britannica, 2018). As a fluid moves between two sections of a channel, the head in point (A) is equal to the head in point (B) plus the head or energy losses between the two sections (due to friction). For gradually varied flow, the change in energy between two sections of a channel can be stated according to equation 10:

𝑧𝐴+ 𝑑𝐴cos 𝜃 + 𝛼𝐴𝑉𝐴2

2𝑔= 𝑧𝐵+ 𝑑𝐵cos 𝜃 + 𝛼𝐵 𝑉𝐵2

2𝑔+ ℎ𝑓 (10)

𝜃, is the slope angle of the channel bottom

𝛼, is an energy coefficient correcting for a non-uniform velocity distribution at each channel section ℎ𝑓, describes the energy loss between the two sections

(Chow, 1959).

The principles introduced can be used to describe the motion of a fluid. The flow of wetlands which can be characterized as open channel flow can be assumed to be steady and gradually varied due to the low flow velocities and small changes in elevation which are typical of wetland environments. This is stated by the principle of continuity, in which for a steady flow, the inflow of water is equal to the outflow.

From the principle of momentum, it can be concluded that changes in momentum (i.e. direction and velocity of a fluid) is due to the action of external forces including the force of gravity, friction, pressure, expansion/contraction of channel cross-sectional geometry and wind shear.

The principle of energy states that the change in energy of a fluid element is due to the work of external forces on the fluid element and the net flux of heat into the element. The principle further states that energy is only transformed between different forms and can neither be created nor destroyed. From the energy equation (of open channel flow for steady, gradually varied flow), and the principle of conservation of energy it can be concluded that the energy is transformed between potential, pressure, kinetic and thermal energy (due to losses). It can further be concluded that the cause of this transformation in energy is mainly due to the work of external forces expressed in the momentum equation (and the net flux of thermal energy into the fluid), i.e. gravity, pressure, friction, contraction/expansion and wind shear.

(22)

The basic driving force of fluid flow is an energy gradient (a difference in energy) between two points in space and time. The direction of transport is from a point of high energy to a point of low energy (USEPA, 2008). An energy gradient (or difference in energy) is produced by changes in energy of a fluid element. Since the changes in energy of a fluid element was due to the work of external forces (neglecting net flux of heat into the fluid), it can be derived that the physical factors which govern the flow pattern or hydrodynamics of wetlands are changes in topography (i.e. where the force of gravity acts), changes in water depth (i.e. where hydrostatic pressure forces acts), the surface roughness of the channel bed and walls (i.e. where the force of friction acts), changes in channel cross-sectional geometry (i.e. where contraction/expansion forces act) and wind (i.e. where wind shear forces act).

1.1.3. The hydrodynamics of wetlands

The treatment efficiency in wetlands is dependent on the hydraulic residence time of the water. A longer hydraulic residence time gives more time for treatment mechanisms in wetlands to take place (see section 1.2.4. for details) which results in a higher treatment efficiency. The hydraulic residence time is in turn dependent on the flow pattern (i.e. the hydrodynamics) (Kjellin et al., 2007). The flow in wetlands can be said to be either ideal or non-ideal. There are two kinds of ideal flow, which are classified based on the mixing regime, i.e. plug flow or instantaneous mixing (Headley and Kadlec, 2007).

In plug flow, there is only lateral mixing and no mixing or dispersion along the axis of the flow path. The result of no longitudinal mixing is that each water parcel spends an equal amount of time in the system and that the entire volume is used to the same extent (Kjellin et al., 2007, Headley and Kadlec, 2007). Under steady-state conditions, a plug-flow system only has a single residence time (equal to the ratio of the volume of the wetland and the average of the inflow and outflow rates) (Headley and Kadlec, 2007).

In instantaneous mixing, (usually modelled as the continuously stirred steady-state flow tank reactor (CSTR)) the water parcels entering the system are instantaneously mixed with the entire contents of the system. Consequently, the outlet composition of the water will be equal to the composition of a fluid element in the middle of the reactor (Headley and Kadlec, 2007). This leads to any fluid element or particle in the system having the same probability of exiting the system at any point in time. Accordingly, there is a range of residence times as different water parcels will spend a varying amount of time in the system (Headley and Kadlec, 2007).

Plug flow is the most efficient flow regime (from the perspective of treatment efficiency) since the entire volume of the wetland is used to the same extent and each water parcel spends an equal amount of time in the system (Kjellin et al., 2007). In reality however, the flow in wetlands is non-ideal, meaning that the degree of mixing lays somewhere in between the two extreme cases described. The result is that water parcels will arrive at the outlet at different times resulting in a distribution of residence times which can usually be described by a bell-shaped residence time distribution curve (RTD). There are in general two mechanisms affecting the degree of non-ideality of the flow: (1) the development of velocity profiles (vertical or horizontal) and (2) the degree of mixing within the flow (Headley and Kadlec, 2007).

Velocity profiles in fluids develop due to the effect of shear stresses (Escudier, 2018). Shear stress can be defined as any force tangential to the surface area on which it acts (Britannica, 2020). Due to the viscosity of fluids (the ability of a fluid to resist shear stress), a fluid in contact with a surface will adhere to the surface and move with the same velocity as the surface, also referred to as the no-slip

(23)

condition. Regarding a moving fluid as a set of layers, each with a velocity u, the velocity of the layer which adheres to a non-moving surface will be zero(Escudier, 2018). The velocity will increase for each layer in a direction normal to the surface while the shear stress will decrease proportionally. The result is the development of a velocity profile (Escudier, 2018). The shape of the profile will depend on whether the flow is laminar or turbulent (Slooff, 2015).

Since shear stresses and thereby also velocity profiles may develop when a moving fluid is in contact with a surface, any surface in wetlands may cause the development of velocity profiles within the flow (including e.g. the wetland bottom and walls and immersed objects such as plant stems and roots) (Headley and Kadlec, 2007).

Mixing in wetlands can be either vertical or lateral and on small or large scale (Headley and Kadlec, 2007). Mixing can be attributed to several factors (which may interact) including variations in bottom topography, wetland geometry (i.e. cross-sectional and boundary shape, and width of the wetland compared to length), variations in surface roughness (due to bottom morphology,

distribution of vegetation and presence of immersed objects) variability in water depth, the effect of wind on the water surface and inflow and outflow rates (Green, 2016, Kjellin et al., 2007, Headley and Kadlec, 2007).

In general, these variations produce variations in shear stresses within the flow and hence

development of various vertical, horizontal, lateral and longitudinal velocity profiles which in turn results in mixing (Green, 2016, Kjellin et al., 2007). One of the main mixing mechanisms in shallow surface water systems, shear dispersion, arise due to lateral variations in longitudinal velocity profiles (Green, 2016).

Large scale mixing can occur due to changes in bottom topography (and thereby also water depth), distribution of vegetation and channel geometry which affects the distribution of water within wetlands (Kjellin et al., 2007, Wörman and Kronnäs, 2005). Since the shear stress decreases with distance from the surface inducing it (e.g. the bottom surface), deeper zones may act as preferential flow paths whereas water in shallow zones can be expected to be subject to higher shear stresses and thereby also lower flow rates.

Vegetation provides most of the flow resistance in wetlands, controlling most of the flow paths within wetlands (Kjellin et al., 2007). Therefore, little flow of water can be expected within dense plant formations. However, vegetation may contribute to large scale mixing by the formation of preferential flow paths between dense plant formations (Kjellin et al., 2007). The presence of vegetation may also cause small-scale mixing around plant stems. Increased vegetation density may also result in increased lateral displacement of the flow due to increased flow tortuosity and friction (Green, 2016).

The geometry of wetlands may influence large scale mixing due to the creation of isolated volumes of water with little flow through of water. This may occur in wide wetlands (in comparison to its length) with a narrow inlet zone (Wörman and Kronnäs, 2005).

Applied wind shear on the water surface may induce turbulence in the water which results in mixing. Wind shear may also move surface water to one side of the wetland inducing counter currents in deeper water in the opposite direction (Headley and Kadlec, 2007).

(24)

1.1.4. Treatment mechanisms and hydrodynamics

The treatment of contaminated water in constructed wetlands is based on naturally occurring mechanisms provided by the soil, vegetation and associated microbial populations (Vymazal, 2007). The contaminants which are typically treated in wetlands can be grouped as suspended solids, organic matter, nutrients (phosphorus and nitrogen), heavy metals and pathogens (Vymazal et al., 1998).

Suspended solids

Suspended solids are removed by physical processes, i.e. sedimentation and filtration (through soil and vegetation) (Stefanakis et al., 2014b, Vymazal et al., 1998). Sedimentation increases with lower flow velocities and longer hydraulic residence times (Geranmayeh et al., 2018). The settling rate of particles is dependent on the particle size. As the particle size decreases, the settling time required increases. To illustrate, a particle size of 10 μm (e.g. clay particles or algae) has a settling time of 2h/m which can be compared to a particle size of 1 μm (e.g. bacteria) which has a settling time of 8 days/m (Koohestanian et al., 2008). Since wetlands usually have long hydraulic residence times (i.e. several days or weeks), almost all suspended solids have enough time to settle (Vymazal et al., 1998).

Organic matter

Organic matter (OM) (also expressed as BOD or COD, biological or chemical oxygen demand) is removed by physical and biological processes. Particulate organic matter is mainly removed by sedimentation and filtration whereas soluble organic matter is removed by aerobic or anaerobic degradation (Stefanakis et al., 2014b, Vymazal et al., 1998). The removal of organic matter from surface water is important since the degradation process consumes oxygen in receiving waters which may lead to oxygen deficiency (USEPA, 2012).

Aerobic (presence of oxygen) and anaerobic (absence of oxygen) degradation are biological degradation processes. Aerobic degradation is the predominant removal mechanism of organic matter and is performed by chemoautotrophic (uses CO2 as carbon source) or chemoheterotrophic (uses organic carbon as carbon source) bacteria. Chemotrophs attain energy by oxidizing organic matter to produce carbon dioxide and water (Stefanakis et al., 2014b). Aerobic degradation is limited by the amount of dissolved oxygen in the water (which is supplied by diffusion into the water from the atmosphere or is released from the root zone of wetland vegetation). It is a faster process compared to anaerobic degradation which occurs in several steps (Vymazal et al., 1998).

The first step in the anaerobic degradation process is the conversion of organic matter to fatty acids which is carried out by obligate or facultative bacteria. The fatty acids are then degraded by acid- or methane forming bacteria which form either sulphuric acid, carbon dioxide and water or methane gas and water. The methane forming bacteria are sensitive to changes in pH and operate only between a pH ranging between 6,5 to 7,5 (Vymazal et al., 1998).

The removal of organic matter is dependent on several parameters, i.e. the concentration of dissolved oxygen (DO), the hydraulic loading of organic matter, the composition of the OM, pH, temperature and the HRT of the water (i.e. the contact time between the organic matter and the microorganisms) (Vymazal et al., 1998, Kadlec and Reddy, 2001, Stefanakis et al., 2014b). The oxygen supply and temperature affect the degradation rate which increases with a higher DO concentration and higher temperature (Stefanakis et al., 2014b, Kadlec and Reddy, 2001). If the hydraulic loading of organic matter is too high, the concentration of DO might become insufficient which results in a slower degradation process, i.e. anaerobic degradation (Vymazal et al., 1998).

(25)

Nutrients: Phosphorus

Nutrients include phosphorus (P) and nitrogen (N). The removal of P and N from surface water is important to prevent eutrophication in receiving water bodies (Stefanakis et al., 2014b).

Phosphorus may occur as inorganic P (orthophosphate) or organic P which can be in either particulate or soluble form. Particulate P is removed by sedimentation and filtration. Soluble inorganic P can be assimilated into microbial biomass and plant tissue. In general, soluble P can also be removed by adsorption and by the process of precipitation (in which the compound is transformed from soluble to particulate form when reacting with another chemical compound) (Stefanakis et al., 2014b, Wang et al., 2005).

Adsorption and precipitation is considered to be the main removal mechanism of phosphorus in wetlands (Stefanakis et al., 2014b). There are in general two main adsorption mechanisms which are relevant for phosphorus removal: Ion exchange and surface complexation (Gustafsson et al., 2007). Ion exchange is an adsorption mechanism in which ions are bound electrostatically to a charged particle surface, i.e. soil particles or organic matter without forming a chemical bond (Gustafsson et al., 2007). Surface complexes are formed when ions form bonds to reactive groups on the surface of solid particles (Gustafsson et al., 2007).

One example of the precipitation process is the formation of calcium phosphate which may form from calcium and phosphate ions dissolved in water. Precipitation is dependent on several factors such as the concentration of each constituent in the water and pH. If the concentration is too low of e.g. the calcium and phosphate ions, precipitation will not occur (Carlsson et al., 1997).

Reactive surface groups may include carboxylic acid groups found on humic substances (organic matter), hydroxide groups which can be found on a variety of particle surfaces (e.g. soil particles), or the oxygen ligand of Fe-, Al-, or Ca-oxides. The affinity to form surface complexes is affected by electrostatic attraction. Therefore, cations have a higher tendency to form complexes with negatively charged surfaces, whereas anions have a higher tendency to form complexes with positively charged particle surfaces. The surface charge of most particle surfaces is variable and changes with pH. At high pH, the prevailing surface charge is negative whereas at low pH, the prevailing surface charge is positive (Gustafsson et al., 2007). With time, the number of reactive sites available for complex formation decreases as more complexes are formed. Furthermore, the surface charge changes as ions bind to the surface which in turn contribute to a lower affinity for adsorption. In effect, the surface becomes saturated (Gustafsson et al., 2007, Stefanakis et al., 2014b).

P usually occurs in the form of 𝑃𝑂43− in wetlands (Stefanakis et al., 2014b). As it is an anion it may form complexes with the Fe, Al or Ca cations which are found on Fe-, Al-, or Ca-oxide surfaces or reactive groups which have a positive charge. Adsorption of 𝑃𝑂43− is highest around pH 6 and decreases as pH increases and a negative surface charge starts to prevail (Gustafsson et al., 2007). P may also form precipitates with Fe-, Al- and Ca-ions. The formation of precipitates and presence of oxides is however dependent on the oxidation state of the Fe, Al, Ca-ions. At low redox potentials below 250 mV, e.g. 𝐹𝑒3+is reduced to 𝐹𝑒2+ which causes P to deprecipitate back into soluble form. Adsorption and precipitation of P is therefore dependent on the adsorption capacity of the soil, redox conditions and pH.

The adsorption capacity of the soil depends on the soil type (content of oxides, clay minerals and grain size where a smaller grain size results in a larger specific surface area and thereby also a larger number of adsorption sites) (Stefanakis et al., 2014b). The presence of clay minerals, and Al-, Fe-, and Ca-oxides increase the adsorption capacity of the soil and the formation of precipitates with oxides. The adsorption capacity is also dependent on the hydraulic residence time (where a higher

(26)

HRT allows for sufficient contact time between P and the adsorption sites and for precipitates to form) (Stefanakis et al., 2014b).

Nutrients: Nitrogen

Nitrogen may occur in various forms, including organic N, ammonia, ammonium, nitrate and nitrite. The main removal mechanism of nitrogen is a multistep microbial process. In the first step, organic N is converted to inorganic N (e.g. ammonium), which is called ammonification.

Ammonification may occur under both aerobic and anaerobic conditions but is faster in the presence of oxygen. The ammonification rate is dependent on temperature, pH and the C/N-ratio. Optimum pH ranges between 6,5-8,5 (Vymazal et al., 1998, Stefanakis et al., 2014b).

The second step is called nitrification, in which ammonium is oxidized to nitrate by nitrifying bacteria. Nitrification is affected by temperature, pH, alkalinity, inorganic C source, and the supply of oxygen and ammonium. Optimal pH ranges between 7,5-8,6 and the optimum temperature ranges between 25-35 C. The minimum temperature for growth of nitrifying bacteria (Nitrosomonas and Nitrobacter) is 5 C and 4 C (Vymazal et al., 1998, Stefanakis et al., 2014b). It should be noted that alkalinity is consumed in the nitrification process. Therefore, it may be important to monitor the alkalinity and pH of the water to maintain optimal conditions in order to maintain favourable conditions for the nitrifying bacteria. Also worth noting, is that competition of dissolved oxygen may occur between degraders of organic matter and nitrifying bacteria since both processes require oxygen (Stefanakis et al., 2014b).

Nitrification is followed by denitrification in which denitrifying bacteria reduce nitrate to nitrite and finally to nitrogen gas. Ammonia and nitrogen gas may volatilize and depart to the atmosphere. Denitrification requires anaerobic or anoxic (absence of molecular oxygen) conditions and a sufficient supply of carbon source. Factors influencing denitrification include absence of dissolved oxygen, redox potential, temperature, pH, and supply of carbon source. Optimum pH ranges between pH 7-8 and reaction rates are very slow below 5 C (Stefanakis et al., 2014b).

Other forms of nitrogen removal include plant and microbial uptake and temporary adsorption of ammonium to soil particles (Vymazal et al., 1998).

Heavy metals

Heavy metals may be removed by sedimentation, filtration, adsorption, precipitation and plant uptake (Vymazal et al., 1998). Metal ions have a positive charge and therefore have a higher affinity for adsorption to surfaces with a negative charge (Gustafsson et al., 2007). Adsorptive surfaces in wetlands with a negative surface charge includes soil particles, humic substances and oxides. Humic substances and oxides have a variable charge which becomes negative with increasing pH

(Gustafsson et al., 2007). Hence, a higher pH creates favourable conditions for cations to adsorb by ion exchange or form surface complexes. It should be noted that adsorption is affected by

competition with other ions. Humic substances (organic matter) which may act as an adsorption site is also an ion which may adsorb to e.g. positively charged oxides (Gustafsson et al., 2007).

Redox processes are chemical reactions which govern the oxidation state and thereby the form or specie of chemical compounds. Consequently, redox processes may affect the affinity for adsorption and formation of precipitates of e.g. metal ions (Gustafsson et al., 2007). Another example is arsenic which may occur in two main redox forms, i.e. arsenate and arsenite. Under reducing redox

conditions, arsenite is the predominating form which has less affinity to adsorb to oxides compared to arsenate. It is therefore more toxic and more mobile compared to arsenate (Gustafsson et al., 2007). Another negative effect of reducing redox conditions, in the case of arsenic, is that oxides may dissolve. The result is a decrease in the number of available adsorption sites for various

(27)

compounds such as metal ions which may be released back into solution (Gustafsson et al., 2007). However, under reducing conditions, sulphur precipitates may form, which also may immobilize metal ions (Gustafsson et al., 2007)

Pathogens and other contaminants

The final two groups of contaminants include pathogens and a new group of contaminants, commonly referred to as emerging contaminants (Vymazal et al., 1998, Ghimire et al., 2019). Pathogens such as bacteria and viruses may be removed from wastewater by predation, excretion of antibiotics from plants, natural die-off, UV-irradiation, filtration and sedimentation (Vymazal et al., 1998).

A new group of contaminants, so called emerging contaminants, include compounds found in various products such as pharmaceuticals, personal care products, industrial compounds, nanomaterials and paint etc. (Ghimire et al., 2019). Currently, there is limited monitoring of this group of contaminants and consequently also limited knowledge of their fate and behaviour in the environment (Ghimire et al., 2019). However, these compounds have been shown to have negative effects on e.g. aquatic organisms and should therefore be treated prior to discharge of wastewater (Ghimire et al., 2019).

The overall treatment efficiency of wetlands

The overall treatment efficiency of wetlands is highly dependent on the degree of non-ideality of the flow. Water parcels passing quickly through the wetland (due to existence of velocity profiles and mixing effects along the flow path of the water have limited interaction with microorganisms and reactive surfaces which result in poorer treatment. These water parcels can be said to have experienced short-circuiting with regard to the theoretical or nominal hydraulic residence time (nHRT) (Headley and Kadlec, 2007). It can be summarized from this section that low flow velocities and a sufficient hydraulic residence time is crucial for suspended solids to have time to settle and for adsorption and precipitation mechanisms to occur. A sufficient HRT is also important to allow for microbial degradation processes and conversion of compounds to take place. This is particularly important in colder climates and at lower DO concentrations which slow down reaction rates and degradation processes.

Other factors which are not related to the hydraulic residence time but also impact the overall treatment efficiency include the mixing of the water and the presence of vegetation. The mixing of the water by wind effects and waves increases the diffusion of DO into surface waters from the atmosphere) (NOAA, 2020). Vegetation play an important role in wetlands since they supply oxygen to the water via the roots but also since they constitute a surface onto which microorganisms can attach, increasing the surface area where treatment mechanisms can be performed (Kjellin et al., 2007).

(28)

2. Materials and Methods

2.1. Conceptual model

A conceptual model of a hydrologic system summarizes what is known about the system and may form a basis for numerical modelling. The conceptual model should describe the system under investigation in a manner which is as simple as possible without losing accuracy in describing system behaviour (Anderson et al., 2015). What to include in the conceptual model and the level of detail depends on the type of hydrological system that is being investigated, available data, purpose of the numerical modelling and the data requirements of the model used (Anderson et al., 2015, Harding, 2014). The purpose of the modelling and availability of data further determines the selection of assumptions and simplifications which needs to be made (Anderson et al., 2015). Conceptual models have commonly been used to describe hydrogeological systems but have also been used to describe wetland systems (Anderson et al., 2015, Harding, 2014).

Since the purpose of modelling was to determine the hydrodynamics of the Löt wetland, the procedure suggested by Anderson et al. (2015) and Earon and Bacharyatta (2018) for the development of conceptual models for groundwater systems was adapted for wetland systems. The adaptation was made based on relevant hydrological factors for wetlands suggested by Harding (2014), the data requirements for the numerical model used which was developed by Kjellin et al. (2007) and the physical factors identified to govern the flow of wetlands (see section 1.2.3.).

Accordingly, the following procedure was used to develop a conceptual model of the wetland system: (1) To identify system boundaries and their hydraulic nature (i.e. constant head or flux boundary), (2) to identify recharge and discharge areas, (3) to identify sources of inflow and outflow of the system, (4) to define the bottom topography of the area, (5) to divide the wetland into sub-domains with homogenous flow resistance conditions, (6) setting of numerical values for boundary conditions and flow resistance, and (7) to identify any missing information and make appropriate assumptions based on the information available.

(1) The system boundaries of the wetland were determined based on orthophotographs and a field visit to confirm the approximate location. Boundary conditions were defined in the numerical model to be either of the type Dirichlet (a known boundary flux) or von Neumann (a known hydraulic potential). The type of boundary condition assigned to each boundary segment was determined based on a water balance of the system. The water balance provided information on what flow components that were relevant to include as input and output to and from the system. Values of constant flux boundaries was determined based on the water balance and information on inflow and outflow rates of wastewater provided by SÖRAB. In the case of a known hydraulic potential, values were determined with the use of a GNSS (Global Navigation Satellite System) receiver (which uses satellites to determine the elevation and position of a geographic point).

(2) Recharge and discharge areas of the wetland (i.e. the inlet and outlet) were identified based on information provided by SÖRAB and by study of topographical maps. Impermeable embankments had been constructed in areas with low elevation surrounding the wetland to prevent outflow elsewhere. The location of the inlet and outlet zones was consistent with the topography of the area (considering the embankments), where recharge areas usually are located in areas of higher elevation whereas discharge areas are located in areas of lower elevation (Gannett, 2007).

(3) In order to determine the inflow and outflow components of the system, two water balances were made: one for surface water and one for groundwater. The general water balance of any

(29)

hydrological system is based on the continuity equation (see equation 11) and can be formulated as the inflow being equal to the outflow plus the time (t) rate of change of storage (S) of the hydrological system (Hendriks, 2010):

𝐼𝑛 = 𝑂𝑢𝑡 +∆𝑆

∆𝑡 (11)

The water balance is defined for a specific time period and for a specified area (Hendriks, 2010). The components of the general water balance equation for an arbitrary hydrologic system include inflow as inflow of surface water (𝑄𝑖𝑛), precipitation (𝑃), surface runoff from the catchment area (𝑅𝑖𝑛), as well as subsurface and groundwater inflow from the catchment area (𝐺𝑖𝑛). Outflow and losses from the system include surface water outflow (𝑄𝑜𝑢𝑡), groundwater and subsurface water outflow (𝐺𝑜𝑢𝑡), evaporation (E), transpiration (T) and interception (I) (EU, 2015, SMHI, 2017).

The first step in calculating the water balance was to determine the area and time span for which each water balance would be defined. Both the surface water balance and the groundwater balance were performed based on annual mean values of the relevant components. The area, however, was not the same for both balances. The software ArcMap (a Geographical Information Systems tool) was used to delineate the sub-watershed of which the wetland is part and the catchment area surrounding the wetland from topographical data using the procedures suggested by Tufts University (2012) and Trent University (2014) respectively. The area defining the surface water balance was estimated in short by defining a flow accumulation grid. The tool Pour Point was then used to find the area which drained to the wetland. Areas which drained to sections with impermeable embankments along the wetland border were excluded (see Fig. 4). The catchment area of the surface water balance amounted to 45 504 m^2.

(30)

Figure 4: The surface water balance was defined for the area (marked in blue hatches) contributing with surface runoff to the wetland, excluding the flow paths which were blocked by impermeable embankments along the remaining boundary segments.

The groundwater balance was defined for the whole sub-watershed surrounding the wetland (see Fig. 5). The area amounted to 173 554 m^2. The wetland area was 31 986 m^2.

(31)

Figure 5: The groundwater balance was defined for the whole sub-watershed surrounding the wetland (marked with blue hatches).

In order to determine what components to include as sources of inflow and outflow and which components were negligible, each component was estimated except for interception and transpiration due to missing data. Data on inflow and outflow rates of surface water, i.e. wastewater from the facility defined as 𝑄𝑖𝑛 and 𝑄𝑜𝑢𝑡, was provided by SÖRAB for the time period of week 1 until the end of week 8 for the year of 2020. These values were scaled up to correspond to annual mean values. The estimation of 𝑃, 𝐺𝑖𝑛, 𝑅𝑖𝑛, 𝐺𝑜𝑢𝑡, and E was based on metrological data from the Swedish Metrological and Hydrological Institute (SMHI).

(32)

The estimated annual precipitation and evaporation over the area for 2019 was approximately 800 mm and 400 mm (SMHI, 2019, SMHI, 2013). The groundwater recharge (i.e. precipitation which was infiltrated) and the surface runoff were estimated by applying the concept of effective precipitation and estimating abstractions by the use of runoff coefficients.

Effective precipitation can be defined as the part of the observed precipitation which is neither retained on the land surface nor infiltrated into the soil and i.e. becomes surface runoff (Chow, 1988). The difference between the total observed precipitation and the effective precipitation can be referred to as abstractions or losses. Abstractions include primarily infiltration into the soil, interception and surface storage in e.g. depressions (Chow, 1988). The abstractions can be estimated by various methods. One way is to use runoff coefficients which can be defined as the ratio of runoff to rainfall over a given time period (Chow, 1988). The catchment area of the wetland was mainly covered by forest. Therefore, typical values of runoff coefficients (RC) for forested land was applied. The value of runoff coefficients for forested land may range between 0,05-0,20 (Goel, 2011). The surface runoff was therefore estimated as a range (see Table 3).

In the surface water balance, the input of surface water included three components, i.e. input of wastewater, effective precipitation falling on the wetland surface area as well as effective precipitation falling on the catchment area which was not blocked by the impermeable embankments and therefore contributed as surface runoff (see Fig. 4). Losses included evaporation and outflow of wastewater. The recharge by surface runoff from the catchment area (𝑅𝑐𝑎𝑡𝑐ℎ𝑚𝑒𝑛𝑡) and the recharge by precipitation falling on the wetland surface (𝑅𝑤𝑒𝑡𝑙𝑎𝑛𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒) were estimated according to equation 12 and 13:

𝑅𝑐𝑎𝑡𝑐ℎ𝑚𝑒𝑛𝑡= (𝑃 − 𝐸𝑇) ∗ 𝐴𝑐𝑎𝑡𝑐ℎ𝑚𝑒𝑛𝑡∗ 𝑅𝐶 (12) 𝑅𝑤𝑒𝑡𝑙𝑎𝑛𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒= (𝑃) ∗ 𝐴𝑤𝑒𝑡𝑙𝑎𝑛𝑑 (13)

Limited information was available regarding groundwater flow. Therefore, the purpose of the groundwater balance was to determine whether or not the inflow of groundwater to the system had the potential of being balanced by the outflow of groundwater. The recharge area of the groundwater within the sub-watershed was estimated by studying geological and hydrogeological maps (including soil type, soil depth, bedrock and fracture zones) provided by the Swedish Cadastral Survey (Lantmäteriet). Most of the sub-watershed area was covered by sandy till, followed by rock outcrops and a small area covered by clay. Since such a large part of the area was covered by till it was assumed that rain falling on bedrock and clay would eventually also infiltrate. In effect, all of the precipitation that did not become surface runoff was therefore assumed to infiltrate and contribute to the groundwater recharge.

Groundwater flow is governed by a hydraulic gradient, a difference in head or energy (measured in m) between two points in space and time (Delleur, 2016). Since groundwater flow velocities are generally small, the total energy or head in a point is equal to the sum of the pressure head and potential energy head (neglecting the velocity head due to low flow velocities) (Chow, 1988). The flow direction is from a point of high hydraulic head to a point of low hydraulic head (Delleur, 2016). Hence, if the pressure level in the till aquifer below and around the wetland is higher than or equal to the pressure exerted by the volume of water within the wetland, there should be no outflow of groundwater from the wetland bottom and

(33)

vice versa. An attempt to estimate the groundwater balance of the sub-watershed and wetland was made by comparing the groundwater recharge of the sub-watershed area to the potential outflow of groundwater from the wetland bottom. The potential outflow of groundwater from the wetland was estimated according to equation 14 as the hydraulic conductivity (K [m/s]) of till times the surface area of till covering the bottom of the wetland (see equation 14). The hydraulic conductivity of sandy till may range between 8 – 10^-6 m/s (SGI, 2008).

𝐺𝑅𝑒𝑐ℎ𝑎𝑟𝑔𝑒 𝑤𝑒𝑡𝑙𝑎𝑛𝑑 = 𝐾𝑇𝑖𝑙𝑙∗ 𝐴𝑤𝑒𝑡𝑙𝑎𝑛𝑑 𝑏𝑜𝑡𝑡𝑜𝑚 (𝑡𝑖𝑙𝑙) (14) The groundwater recharge of the catchment area was estimated by considering surface runoff as an abstraction from effective precipitation instead of infiltration which resulted in the following equation (equation 15):

𝐺𝑅𝑒𝑐ℎ𝑎𝑟𝑔𝑒 𝑐𝑎𝑡𝑐ℎ𝑚𝑒𝑛𝑡= (𝑃 − 𝐸𝑇) ∗ 𝐴𝑐𝑎𝑡𝑐ℎ𝑚𝑒𝑛𝑡∗ (1 − 𝑅𝐶) (15) (4) The bottom topography of the wetland was defined by interpolating collected water depth

point data using the ArcMap tool Topo to Raster. The continuous surface of water depth produced was then subtracted from the mean observed water surface elevation along the wetland border which was 38,1 m.a.s.l. Hence, a continuous digital elevation model of the bottom topography could be obtained with sea level as reference datum (see Fig. 7). (5) The wetland was divided into seven different homogenous sub-domains with respect to flow

resistance based on orthophotographs of the vegetation distribution within the wetland confirmed by a field survey (see Fig. 8) since vegetation is the main source of flow resistance in wetlands, according to Kjellin et al. (2007). The sub-domains were more specifically created by digitizing polygons in ArcMap based on an orthophotograph of the wetland, following the outline of the vegetation distribution within it. The subdomains included areas of open water, dense reed beds, less dense reed beds, flow through a pipe through the permeable gravel embankment intersecting the wetland as well as porous medium flow through the embankment itself (see Fig. 8).

The flow resistance of each subdomain was calculated according to equation 16 suggested by Wörman and Kjellin (2020) where each parameter is presented in Table 1.

𝐹 =𝛼𝑘𝑚𝜐𝑛 2𝑔 (16) where 𝛼, 𝑖𝑠 𝑎 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 [−] 𝑚, 𝑖𝑠 𝑎 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 [−] 𝑛, 𝑖𝑠 𝑎 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 [−] 𝑘, 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑜𝑢𝑔ℎ𝑛𝑒𝑠𝑠 ℎ𝑒𝑖𝑔ℎ𝑡 [−] 𝜐, 𝑖𝑠 𝑡ℎ𝑒 𝑘𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑎𝑚𝑏𝑖𝑒𝑛𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 [𝑚2 𝑠 ]

(34)

𝑔, 𝑖𝑠 𝑡ℎ𝑒 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 [𝑚 𝑠2]

The roughness height of the wetland bottom, k, was set equal to the roughness height of a natural river bed for which k = 0,1 – 3,0 [ft] and 0,0008-0,0180 [ft] for cast iron which the pipe was assumed to be made of (Chow, 1959). These values were converted to [m] where 1 foot was taken as 0,3048 m.

In equation 16, for laminar flow, n is equal to 1 and for turbulent flow, n tends to 0 (Wörman and Kjellin, 2020). For porous medium flow or flow through vegetation such as a reed or cattail bed, m can be set equal to -2. For open water flow, m was found to be equal to -1,46 for part of the

Everglades wetland. If equation 16 should describe the Manning equation, which is applied to open channel flow, m can also be set equal to -1/3 which was assumed here (Wörman and Kjellin, 2020). The mean stem diameter of the cattail plants was assumed to be 0,005 m since there were both thinner and thicker stems present within the wetland. The average spacing of the dense reed bed was assumed to be 0,01 m and the average spacing of the less dense reed bed was assumed to be 0,05 m (Kadlec, 2019).

The kinematic viscosity for water was found to be 1,785 ∗ 10−6 m2

s and 1,519 ∗ 10 −6 m2

s for 0 and 5 ℃ respectively (Street, 1996). Here, the kinematic viscosity of water at 5 ℃ was assumed to be applicable. As mentioned earlier, a summary of all values used in equation 16 is presented in Table 1. The flow resistance values were calculated according to equation 16 as the mean of the flow resistance with high and low roughness height values (see Table 6).

The parameter alpha (in equation 16) was determined either from a previous study or calculated by equation 17. For laminar sheet flow, 𝛼 was found to be equal to 24 which also was assumed to be applicable for open water flow here (Wörman and Kronnäs, 2005). For vegetation, such as reed beds, 𝛼 can be approximated by equation 17, also suggested by Wörman and Kronnäs (2005). The mean water depth which was required to calculate alpha is presented in Table 1.

𝛼 = 40𝑑ℎ

𝑠2 (17)

where

d, is the stem diameter of a reed plant [m] h, is the mean water depth of the reed bed [m] s, is the spacing between stems [m]

References

Related documents

The increasing availability of data and attention to services has increased the understanding of the contribution of services to innovation and productivity in

Parallellmarknader innebär dock inte en drivkraft för en grön omställning Ökad andel direktförsäljning räddar många lokala producenter och kan tyckas utgöra en drivkraft

Närmare 90 procent av de statliga medlen (intäkter och utgifter) för näringslivets klimatomställning går till generella styrmedel, det vill säga styrmedel som påverkar

• Utbildningsnivåerna i Sveriges FA-regioner varierar kraftigt. I Stockholm har 46 procent av de sysselsatta eftergymnasial utbildning, medan samma andel i Dorotea endast

I dag uppgår denna del av befolkningen till knappt 4 200 personer och år 2030 beräknas det finnas drygt 4 800 personer i Gällivare kommun som är 65 år eller äldre i

Den förbättrade tillgängligheten berör framför allt boende i områden med en mycket hög eller hög tillgänglighet till tätorter, men även antalet personer med längre än

På många små orter i gles- och landsbygder, där varken några nya apotek eller försälj- ningsställen för receptfria läkemedel har tillkommit, är nätet av

Det har inte varit möjligt att skapa en tydlig överblick över hur FoI-verksamheten på Energimyndigheten bidrar till målet, det vill säga hur målen påverkar resursprioriteringar