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MODELING THE LONGEVITY OF INFILTRATION SYSTEMS FOR PHOSPHORUS REMOVAL Lin Yu January 2012 TRITA-LWR Degree Project 12:01 ISSN 1651-064X LWR-EX-12-01 Modeling the Longevity of Infiltration System for Phosphorus Removal © Lin Yu 2012 Degree Project for master program in Water System Technology Environmental Geochemistry and Ecotechnology Department of Land and Water Resources Engineering Royal Institute of Technology (KTH) SE-100 44 STOCKHOLM, Sweden Reference should be written as: Lin, Y (2012) “A Modeling Method for Longevity Study of Infiltration System for Phosphorus Removal” TRITA LWR Degree Project 12:01, 39 p ii Lin Yu TRITA LWR Degree Project 12:01 S UMMARY IN S WEDISH En ny modell metod för uppskattning av livslängden för infiltration system som föreslås i denna studie. Modellen var en-dimensionell, baserat på resultat från långfristiga infiltration platser i Sverige, med vissa fysiska och kemiska parametrar som styrande faktorer. Den definierar livslängden för infiltration system som den tid under vilken P lösningen i effulent är under nationella kriterier (1 mg / L i denna studie), och det syftar till att ge livslängden för en viss punkt i infiltration systemet. Marken i modellen antas vara helt homogen och ISO-tropism och vattenflöde antogs vara omättat flöde och konstant ständiga inflödet. Flödet beräknades från den svenska kriterierna för infiltration system. Den dominerande processen i modellen skulle vara lösta transporten processen, men skulle utvecklingsstörning styrs av sorption spela en viktigare roll än advektion och dispersion för att bestämma livslängden i modellen. Genom att använda den definition av ett långt liv i denna studie var livslängd tre jordkolonner vid 1 m djup (Knivingaryd, Ringamåla och Luvehult) 1703 dagar, 1674 dagar och 2575 dagar. Konsumtion tiden för tre jordkolonner i inflödet av 5 mg / l 2531 dagar, 2709 dagar och 3673 dagar. Den beräknade sorberas fosfor kvantitet för jord från platser Kn, Lu och Ri när de når uppskattade livslängd var 0,177, 0,288 och 0,168 mg / g, medan den maximala sorption av Kn, Lu och Ri var 0,182, 0,293 och 0,176 mg / g separat. Från resultatet av känslighetsanalyser av modellen var sorption kapacitet och flödeshastighet som är viktigast för livslängd infiltration systemet. Lägre strömningshastighet och högre P sorption kapacitet förlänga livslängden för en infiltration säng. På grund av sorption isoterm valts i denna studie och antagandet om omedelbar jämvikt, var sorption graden av jorden kolumnen ganska linjär, även om den beräknade livslängden var betydligt kortare än den verkliga utmattning tid på jorden kolumnen. Faktum är att jorden har nästan nått sitt sorption maximalt när systemet når sin livslängd. iii Modeling the Longevity of Infiltration System for Phosphorus Removal iv Lin Yu TRITA LWR Degree Project 12:01 A CKNOWLEDGEMENTS First of all, I would like to thank my supervisor Jon Petter Gustafsson, who helped me a lot with all the lab work designing and preliminary data processing. His suggestions on literature reading really helped me learn about the processes and construct the idea of my model. I also want to thank Professor Per-Erik Jansson for his precious advices during my modeling work. His rich experiences and constructive suggestions really saved me lots of time and lead me to the right way of building the model. Moreover, I also would like to express my special thanks to David Eveborn and Elin Elmefors. Because of their hard work, I got the possibility to work on the soil samples for my thesis. And it is really happy to work with them in the labs of SLU in Uppsala, although it was really hard work back then, I am so greatful to work with them. Last but not least, I would like to thank David Gustafsson who helped me know more on the hydrogeology process in the subsurface, and Professor Gunno Renman, from whose articles I got really inspired about the phosphorus sorption process, and I really appreciate his appreciation on my thesis work. Finally, thank all the persons who helped and cared about me during my study in KTH. 爸爸媽媽，我愛你們！ v Modeling the Longevity of Infiltration System for Phosphorus Removal vi Lin Yu TRITA LWR Degree Project 12:01 T ABLE OF C ONTENT Summary in Swedish ........................................................................................................ iii Acknowledgements ............................................................................................................v Table of Content .............................................................................................................. vii Nomenclature ................................................................................................................... ix Abstract .............................................................................................................................. 1 1. Introduction ............................................................................................................. 1 Phosphorus chemistry ....................................................................................... 2 Sorption and desorption of inorganic phosphorus .......................................... 2 Literature review and study objective............................................................... 3 Contaminant Solute Transport Equation......................................................... 5 1.4.1. Parameters in the Advection Dispersion Equation .................................................. 6 2. Material and methods ............................................................................................. 9 2.1. Site description and field sampling .................................................................. 9 2.2. Analytical work................................................................................................. 10 2.2.1. Oxalate-soluble iron and aluminum ....................................................................... 10 2.2.2. Batch experiment .................................................................................................. 10 2.3. Parameters for Modeling ................................................................................. 12 2.3.1. Flow velocity ......................................................................................................... 12 2.3.2. Retardation factor ................................................................................................. 12 2.3.3. Hydrogeological Parameters .................................................................................. 13 2.4. Numerical solution scheme ............................................................................ 14 2.5. Model description ............................................................................................ 15 2.5.1. Modeling tools ...................................................................................................... 16 2.5.2. Modeling scenarios................................................................................................ 16 3. Results .................................................................................................................... 17 3.1. Oxalate extraction ............................................................................................ 17 3.2. Batch Experiments .......................................................................................... 19 3.2.1. Phosphorus sorption experiments ......................................................................... 19 3.2.2. pHdependence experiments .................................................................................. 22 3.2.3. Chemical Speciation Results .................................................................................. 25 3.3. Modeling results .............................................................................................. 26 3.3.1. Calculated Model Inputs ....................................................................................... 26 3.3.2. Longevity prediction of Kn, Lu and Ri .................................................................. 26 3.3.3. Effect of the Modeling time .................................................................................. 27 3.3.4. Effect of the Soil Sorption Capacity ...................................................................... 27 3.3.5. Effect of inflow concentration and background concentration .............................. 29 3.3.6. Sensitivity analysis of soil properties ...................................................................... 30 3.3.7. Sorption capacity study and sorption velocity ........................................................ 31 3.4. D I S C U S S I O N O N M O D E L I N G R E S U L T S .................................................. 33 3.4.1. Factors influencing the longevity of soil column .................................................... 33 3.4.2. Longevity of infiltration bed and evaluations with current method ........................ 34 4. Further study ......................................................................................................... 35 4.1. Boundary Condition ........................................................................................ 35 4.2. Flow velocity & hydrogeology ........................................................................ 35 4.3. Desorption & Operation Mode ....................................................................... 35 4.4. Influence of pH ................................................................................................ 36 References ........................................................................................................................ 37 Other references............................................................................................................... 39 Apendix I – Measured dry weight of soil samples .......................................................... 1 1.1. 1.2. 1.3. 1.4. vii Modeling the Longevity of Infiltration System for Phosphorus Removal Apendix II – Measured oxalate-soluble phosphorus of soil samples ............................ 2 Appendix III: Batch Experiment lab design ................................................................... 3 Series A - 5d equilibration of soils. .............................................................................. 3 Series B - 5d equilibration of soils. .............................................................................. 4 Series C - 5d equilibration of soils. .............................................................................. 5 Appendix IV: Empirical data for porosity calculation .................................................... 6 Appendix V: Comparison of desorbedP........................................................................... 7 Appendix VI: Matlab Codes for Modeling ...................................................................... 8 pdeadeT.m: main m-file for the solution of the ADE equation in the model .......... 8 Isotherm.m: the m-file for isorthem plotting ............................................................. 9 Soilp.m: the m-file for calculation of soil property parameters .............................. 12 MultiLineReg.m: the m-file for the multi-linear regression of the data ................. 13 viii Lin Yu TRITA LWR Degree Project 12:01 N OMENCLATURE A cross-section area of control volume longitudinal and transverse dispersivity αL, αT β kinetic rate constant for sorption C solute concentration in water phase Cini the original phosphorus in soil matrix solute concentration in solid phase CS DL, DT longitudinal and transverse dispersion coefficient D* molecular bulk diffusion coefficient h time step in discretization of PDE I coefficient for C in Freundlich equation ψ water tension k distance step in discretization of PDE K hydraulic conductivity * diffusion coefficient K dispersion coefficient (partitioning coefficient) Kd KF coefficient in Freundlich equation L longevity of infiltration beds dry weight of soil Ms Mt total mass of soil n porosity ne effective porosity θ volumetric water content ρ density bulk density of soil ρb ρs particle density of soil q Darcy’s flux R retardation factor S phosphate sorption in equilibrium state phosphorus sorption capacity Spsc phosphorus sorption in modeling soil column Stotal average pore velocity ux v Darcy’s velocity V volume of the substrate per person specific discharge in longitudinal, lateral and vertical directions Vx,y,z ix Modeling the Longevity of Infiltration System for Phosphorus Removal x Lin Yu TRITA LWR Degree Project 12:01 A BSTRACT A new modeling method for estimation of the longevity of infiltration system was suggested in this study. The model was one-dimensional, based on results from long-term infiltration sites in Sweden, taking some physical and chemical parameters as controlling factors. It defines the longevity of infiltration systems as the time during which the P solution in effulent is under national criteria (1 mg/L in this study), and it aims at providing the longevity for any given point of the infiltration system. The soil in the model was assumed to be totally homogenous and isotropic and water flow was assumed to be unsaturated flow and constant continuous inflow. The flow rate was calculated from the Swedish criteria for infiltration systems. The dominant process in the model would be the solute transport process; however, retardation controlled by sorption would play a more important role than advection and dispersion in determining the longevity in the model. By using the definition of longevity in this study, the longevity of the three soil columns at 1 m depth (Knivingaryd, Ringamåla and Luvehult) were 1703 days, 1674 days and 2575 days. The exhaustion time of the three soil columns under inflow of 5 mg/L were 2531 days, 2709 days and 3673 days. The calculated sorbed phosphorus quantity for soil from sites Kn, Lu and Ri when they reach estimated longevity were 0.177, 0.288 and 0.168 mg/g, while the maximum sorption of Kn, Lu and Ri were 0.182, 0.293 and 0.176 mg/g separately. From the result of sensitivity study of the model, the sorption capacity and flow velocity were most important to the longevity of the infiltration system. Lower flow velocity and higher P sorption capacity extend the longevity of an infiltration bed. Due to the sorption isotherm selected in this study and the assumption of instant equilibrium, the sorption rate of the soil column was quite linear, although the estimated longevity was much shorter than the real exhaustion time of the soil column. In fact the soil has almost reached its sorption maximum when the system reaches its longevity. Key words: phosphorus sorption isotherm; infiltration system; transport model; longevity. 1. I NTRODUCTION Phosphorus in high concentrations is considered to be one controlling factor of eutrophication of natural water bodies. Since 1960s, the concentrations of phosphorus (P) and nitrogen (N) have increased worldwide as a result of agricultural application of manure and synthetic fertilizers and input of wastewater (Appelo and Postma, 1996). Society starts to pay more attentions on the removal of nutrients by applying different technics to wastewater treatment systems. Septic tank systems with soil infiltration are widely used for on-site domestic wastewater disposal in rural and isolated communities as well as in many unsewered urban localities (Cheung and Venkitachalam, 2006). Artificial infiltration beds can be used when natural soil exhibits inadequate drainage or pollutant attenuation. In recent research, an increasing number of filter materials have proved to be suitable media for P removal in on-site wastewater treatment systems. Batch experiments and column experiments are run to test the phosphorus sorption capacity (PSC) of filter materials, which can be regarded one important criterion for the selection of filter materials (Cucarella and Renman, 2009). However, conventional on-site sys1 Modeling the Longevity of Infiltration System for Phosphorus Removal tems are still using soil or gravel as filter materials, in this situation, poor phosphorous retention is often noted and P entering groundwater can subsequently cause eutrophication problems in streams, lakes and estuaries. There are approximately 850 000 onsite systems in Sweden. 1/3 has no treatment or only septic tanks. An additional 250 000-300 000 systems (about 1/3) have poor treatment and needs improvement. Only the remaining 1/3 are using traditional P removal techniques as soil filters or soil infiltration (Johansson, 2008). The Swedish framework for regulation of on-site treatment systems was updated in 2006 and 2008. One specification is that on-site systems need to reduce BOD7 and phosphorus by 90% and nitrogen by 50% in sensitive areas, whereas systems in other areas must reduce BOD7 and phosphorus by 90% and 70% respectively (Weiss et al., 2008). The performance of the on-site infiltration systems remains unknown. David Eveborn and Deguo Kong’s research about the performances of several long-term infiltration beds in south Sweden indicates that the removal of phosphorus in long-term septic systems is really disappointing; a removal rate of only about 8% was reported for an open infiltration system operating over a period of 16 years (Kong, 2009; Eveborn et al., 2009). The estimation of the longevity of these infiltration beds therefore is crucial for a correct assessment of the operation of septic systems. 1.1. Phosphorus chemistry In the lithosphere, phosphorus occurs predominantly as phosphates, PO4-3, although a rare iron-nickel phosphide, schreibersite ((Fe, Ni)3P8) is also known in nature (Hocking, 2006). Orthophosphate is the simplest phosphate, and consists of phosphoric acid (H3PO4) and its dissociate forms. In water, orthophosphate mostly exists as H2PO4- in acidic conditions or as HPO42- in alkaline conditions. Many phosphate compounds are not very soluble in water; therefore, most of the phosphate in natural systems exists in solid form. However, soil water and surface water (rivers and lakes) usually contain relatively low concentrations of dissolved (or soluble) phosphorus (online literature from Minnesota University). In soils, P may exist in many different forms, which in practical terms can be divided into organic P and inorganic P. Water in soil typically contains about 0.05 mg L-1 of inorganic phosphate in solution. Two types of reactions control the concentration of inorganic phosphate in soil solution: precipitation-dissolution and sorption-desorption processes. It is now generally accepted that precipitation-dissolution reactions do not play an important role in controlling the concentration of phosphate in the solution of majority of soils. Thus, the second type of reaction, sorption-desorption, is considered more important (Cornforth, 2009). However, the precipitation of calcium phosphates is considered to be an exception, and recent research (Weiss et al., 2008) has shown that aluminium phosphate precipitation can also influence the concentration of phosphorus in some situations. 1.2. Sorption and desorption of inorganic phosphorus A large number of papers have studied the process of phosphorus sorption in the soil. Sorption refers to simply to the observable uptake of a compound by a material, and can include several different processes such as absorption and adsorption. In adsorption the chemical is bound to the surface of the solid. In absorption, the chemical enters into the matrix of the solid, i.e. diffusing into the solid volume. Concerning the sorption of phosphorus, there is a number of complicating and also un- 2 Lin Yu TRITA LWR Degree Project 12:01 known factors that are as yet not fully understood. A two-step sorption process is accepted by most researchers; it is generally agreed that the first step is fast and reversible (McGechan and Lewis, 2002a; Spiteri et al., 2007; Cheung and Venkitachalam, 2006). The nature of the second, slow, step is much less understood. McGechan and Lewis (2002a) describe the second step as consisting of various slower time-dependent processes, some of which lead to deposition of P at a depth below the surface of particles, while in the study of Spiteri et al. (2007), the slow step consists of slow diffusion into micropores or aggregates or precipitation of metal phosphate phases (Spiteri et al., 2007). Normally the fast step would take very short time, but the slow step takes much longer time and different studies show different times for P sorption to reach equilibrium (Cheung and Venkitachalam, 2006). Opinions also differ about the extent to which the slow step is reversible. Desorption is the reverse of sorption, and it is usually induced by dilution of the soil solution. The desorption process may be very complicated because of the multiple sorption processes, since the extent to which slow deposition has progressed influences the quantity of sorbed material available for fast desorption from the surface sorption sites (McGechan and Lewis, 2002a). As for other reactive inorganic ions, the extent to which P is adsorbed relative to that in solution is highly non-linear. As the chemical affinity towards P varies between different binding sites on the solid surfaces; high-affinity sites becoming occupied before low-affinity sites. This nonlinearity is commonly represented mathematically by a number of empirical equations (‘isotherms’), which can be calibrated after logarithmic or other transformations. The most common sorption isotherms include linear KD model, basic Freundlich, extended Freundlich, Langmuir, Langmuir-Freundlich, Gaines-Thomas and so on (Gustafsson et al., 2007). In this case, desorption is not taken into account in the modeling part because no dilution happen in the system. The status of the sorption is assumed to be in the equilibrium state, since the studied sites have been running for a long time, at least more than 18 years. 1.3. Literature review and study objective There is no standard definition for the longevity of infiltration beds. However, of those studies related with longevity or lifetime of infiltration beds, two main methods are applied. One method used by lots of researchers, is to estimate the longevity of infiltration beds or constructed wetlands by estimating the longevity of phosphorus absorbents. Sakadevan and Bavor pointed out in 1998 that the expected longevity of a constructed wetland can be estimated by using a P sorption maximum; phosphorus sorption capacity (Xu et al., 2006), phosphorus saturation potential (Drizo et al., 2002) or the phosphorus retention capacity (Seo et al., 2005). Of course, this method could be used also to study longevity of some infiltration systems. The equation used in this method is straightforward, L= (1) Psorp Pcons = V × ρ × S psc PPE Where, L = longevity of infiltration beds, T Psorp = total phosphorus that can be removed by substrate, M 3 Modeling the Longevity of Infiltration System for Phosphorus Removal Pcons = total phosphorus been emitted to the substrate, MT-1 V = volume of the substrate per person, L3 ρ = density of substrate, ML-3 Spsc = phosphorus sorption capacity, MM-1 PPE = emission of phosphorus per person, MT-1 Most of studies applying this method (Xu and et al., 2006; Seo et al., 2005; Drizo et al., 2002; Drizo et al., 1999) use the value of emission of phosphorus per person from the study of Laak (1986), i.e. 3g of phosphate (PO4) excreted per person per day with additional 4g discharge from cleaning compounds, giving a total of 7g of PO4 (or 2.3g of P). For the volume of the substrate per person, different countries have different guidance value, mostly used in the literature are 3m3 PE (0.6m in depth, 5m2 in area) and 9m3 PE (0.9m in depth, 10m2 in area). As for Sweden, according to the EC/EWPCA method published in 1990, the volume of substrate per person is 3m3 or 4.5 tons of substrate. The volumetric phosphorus sorption capacity depends on the substrates used. Batch experiments or column experiments are run to measure the quantity of phosphorus sorption. Based on the experiment results, sorption isotherms are applied to calculate the maximum phosphorus sorption of a certain substrate, usually after extrapolation (e.g. Cucarella and Renman, 2009). The other method used to estimate the longevity of infiltration systems is based on the results of column studies. In this kind of studies, researchers set up column experiments to simulate the real infiltration system. Detailed data (effluent phosphorus concentration) are recorded continuously for a long time. Thus, a prediction of longevity of the system is made in agreement with the data. The definition of longevity here is the time during which the effluent concentration is under the national criteria (Heistad et al., 2006; Renman and Renman, 2010). The estimated longevity of infiltration beds is between 7 and 22 years (results are correlated into Swedish standard: 3 cubic meters substrate per person) of all the studies, as showed in the table below. However, there are many uncertainties in both methods. The first method actually estimates the theoretical exhaustion time for an infiltration system, which cannot be equaled to the longevity of the system. As Heistad et al. (2006) pointed out: the effluent concentration should be a key factor to predict the longevity of the infiltration bed. Whereas, the estimation in the second method is a “fine guess” based on specified column experiments; this, indicates the results are not of universal value. For wetland system using Pulverized fuel ash, gravel-based system, light expanded clay aggregates (LECA) and shell-based units are studied, results from the literature indicate a typical life span of constructed wetland system (CWS) for P removal only 2-5 years (Drizo et al., 1999). The current way to estimate longevity ignores certain operational and experimental parameters, such as loading rate, age of system, hydraulic design, temperature and physical and chemical properties of substrates. 4 Lin Yu TRITA LWR Degree Project 12:01 Table 1 Longevity studies from the literature. a the column volume is 6 cubic meters designed for a house. b a system loaded with 1 cubic meter substrates can treat the wastewater of a household with 5 people for at least one year. 3 Longevity V(m ) Spsc(gP/kg) Substrate Source 22 yr 3 8.89 furnace slag Xu et al., 2006 7 yr 3 0.73 shale Drizo et al., 2002 13 yr 3 1.35 EAF steel slag 8 yr 3 0.83 oyster shell Seo et al., 2005 5 yr 1.2 Null Filtralite Heistad et al., 2006 1+ yr 0.2 Null Polonite Renman and Renman, b 2010 a A new modeling method for estimation of the longevity of infiltration system is suggested in this study. The model is one-dimensional, based on results from long-term infiltration sites in Sweden, taking some physical and chemical parameters as controlling factors. It uses Heistad’s definition for longevity, and it aims at providing the longevity for any given point of the infiltration system. 1.4. Contaminant Solute Transport Equation Lots of textbooks about groundwater and pollution have the same equation for solute transport in groundwater, but sometimes with different notations. In reality, lots of different processes can influence the solute concentration in groundwater. When it comes to the solute transport equation, five terms are defined as influencing factors. Advection: advection is the transport of solute by the groundwater flow. The one-dimensional advective transport equation in a homogeneous aquifer can be expressed as: ∂C ∂C = −u x ∂x (2) ∂t , where C = solute concentration, ML-3 t = time, T ux = average pore velocity, ux = q/ne. here q is Darcy’s flux, ne is effective porosity Diffusion: Diffusion is the flux of solute from a zone of higher concentration to one of lower concentration due to the Brownian motion of ionic and molecular species. In steady state, the change of concentration caused by diffusion can be deduced using Fick’s law: (3) ∂C ∂ 2C = K∗ 2 ∂t ∂x , where K* is the diffusion coefficient. Dispersion: Dispersion is the spreading of the plume that occurs along and across the main flow direction due to aquifer heterogeneities at both the small scale (pore scale) and at the macroscale (regional scale). Factors 5 Modeling the Longevity of Infiltration System for Phosphorus Removal that contribute to dispersion include: faster flow at center of the pores than at the edges; some pathways are longer than others; the flow velocity is larger in smaller pores than in larger ones. This is known as mechanical dispersion. The spreading due to both mechanical dispersion and molecular diffusion is known as hydrodynamic dispersion (Delleur, 1999). There is the famous advection-dispersion equation for solute transport problem, which in one-dimension is: ∂C ∂C ∂ 2C = −u x + DL 2 ∂t ∂x (4) ∂t , where DL is the longitudinal dispersion coefficient. Sorption and Reactions: sorption can influence solute transport as well. Normally a retardation factor R is introduced to the equation to express the influence of sorption, which will be discussed in the coming chapter. Reactions include chemical, physical and biological processes which would change the solute concentration in the transport. Those first order reactions such as radioactive decay and degradation would be simple to integrate into the equation, but for complicated second or high order reactions, integration would be very difficult. Then a simplified reaction term can be used in the transport equation, (5) ∂C ∂C ∂ 2C n = −u x + DL 2 ± ∑ rm ∂t ∂x ∂x m =1 The last term on the right side is for reactions. 1.4.1. Parameters in the Advection Dispersion Equation 1.4.1.1Sorption and Retardation factor Soil P can be considered as being contained in a number of ‘pools’, including (amongst others) dissolved inorganic P, inorganic P sorbed onto surface sites, inorganic P sorbed or deposited by various slow timedependent processes and various organic P pools (McGechan and Lewis, 2002a). In this study, organic P pools are ignored because of their low concentration in infiltration systems for wastewater treatment, and inorganic P is divided into only two pools, the one in the water phase and the one in the solid phase, which is highly immobile. So the sorption process can be seen as the process of P in water phase turning into P in solid phase. A control volume with length dx and cross-section area A is defined (Fig. 1). For simplicity, set ∂/∂y = ∂/∂z = 0 and sorption is everywhere at equilibrium. As the system studied is unsaturated, the volumetric water content is θ, and the mean pore velocity is ux. Here the partitioning coefficient (distribution coefficient) Kd is induced to describe the fraction that will sorb onto the solid phase. Kd = concentration associated with solid [mass chemical / mass solid ] Cs = concentration in water[mass / volume water ] C 6 Lin Yu TRITA LWR Degree Project 12:01 Fig. 1. One dimension control volume: blue points reprensent P in solid phase, red points represent P in liquid phase Where Cs is the solute concentration in solid phase (M/M), C is the solute concentration in water phase (M/L3). The conservation of mass for this volume is: ∂M = [uxCA]1 − ∂t ∂C ⎤ ⎡ ⎢⎣−DL ∂x Aθ ⎥⎦ − 1 advection in advection out dispersion at 1 [uxCA]2 + ∂C ⎤ ⎡ ⎢⎣−DL ∂x Aθ ⎥⎦ 2 dispersion at 2 Because advection and dispersion happen only in water, the flux term in the equation only includes the dissolved concentration C. If C and ∂C/∂x are continuous function of x, then approximate C2 = C1 + (∂C/∂x)dx and (∂C/∂x)2 = (∂C/∂x)1 + (∂2C/∂x2)dx. Then equation (5) becomes: ∂M ∂C ∂ 2C = −u x A dx + DL Aθ 2 dx ∂x ∂x (6) ∂t The total mass M consists of both solid and water components, the bulk density ρb is the mass of solid matrix per unit volume, since V = Adx, so the total mass can be written, M = CsρbV + CθV. If Ct = M/V, then (6) becomes, (7) ∂ (Cs ρb + Cθ ) ∂C ∂ 2C = −u x + DLθ 2 ∂t ∂x ∂x Since ρb and θ are not changing with time, one can, after rearranging, get the equation for one-dimensional unsaturated transport including sorption, 7 Modeling the Longevity of Infiltration System for Phosphorus Removal u ∂C ∂C ∂ 2C ρ ∂Cs =− x + DL 2 − b θ ∂x ∂x θ ∂t (8) ∂t As Cs = Kd×C, for the equilibrium state Kd is a constant, so ∂Cs/∂t = Kd(∂C/∂t), then equation (8) becomes, (9) (1 + K d ρb ∂C u ∂C ∂ 2C =− x + DL 2 ) θ ∂t θ ∂x ∂x The retardation factor R is defined as R = 1 + K d ρb , and because ux/θ θ equals the Darcy’s velocity v, so equation (9) can be written, ∂C v ∂C DL ∂ 2C =− + ∂t R ∂x R ∂x 2 (10) 1.4.1.2 Fluid velocity Before the solution of transport equation, the flow equation should be solved first to get the flow velocity of the system. Equations of groundwater flow are derived from consideration Darcy’s law and of an equation of continuity that describes the conservation of fluid mass during flow through a porous material. In this case, unsaturated conditions are assumed for the infiltration system. For flow in an elemental control volume that is partially saturated, the equation of continuity must now express the rate of change of moisture content as well as the rate of change of storage due to water expansion and aquifer compaction. ∂ ( ρ vx ) ∂ ( ρ v y ) ∂ ( ρ vz ) ∂ ( ρθ ) ∂ρ ∂θ + + = =θ +ρ ∂y ∂z ∂t ∂t ∂t (11) ∂x Where ρ = water density, ML-3 vx,y,z = specific discharge in longitudinal, lateral, and vertical directions, LT-1 θ = moisture content t = time, T The first term on the right hand side of equation (11) is negligible and by inserting the unsaturated form of Darcy’s law, in which the hydraulic conductivity is a function of the pressure head, K(ψ), then the equation becomes, upon canceling the ρ term: ∂ ∂h ∂ ∂h ∂ ∂h ∂θ ( K (ψ ) ) + ( K (ψ ) ) + ( K (ψ ) ) = ∂x ∂y ∂y ∂z ∂z ∂t (12) ∂x Hence, after noting that h = z + ψ, and one-dimension condition is applied; the equation turns into the Richards Equation (1931), ∂θ ∂ ⎛ ⎛ ∂ψ ⎞⎞ = ⎜ K (ψ ) ⎜ + 1⎟ ⎟ ∂t ∂x ⎝ ⎝ ∂x ⎠⎠ (13) 8 Lin Yu TRITA LWR Degree Project 12:01 The water retention curve and hydraulic conductivity function are necessary to solve equation (13). 1.4.1.3Dispersion Coefficient Dispersion coefficients are difficult to determine for use in contaminant transport models. They are usually empirical and they are a strong function of scale. Following the treatment of Scheidegger, a scaling factor is used that correlates with a length scale in laboratory soil columns and field tracer tests. The scaling factor is called dispersivity, α. (14) DL = α L u L + D*(a ) DT = αT uL + D* (b) Where DL = longitudinal dispersion coefficient, L2T-1 DT = transverse dispersion coefficient, L2T-1 αL, αT =longitudinal and transverse dispersivity, L uL = longitudinal velocity, LT-1 D* = molecular bulk diffusion coefficient, L2T-1, is on the order of 105cm2s-1 (Schnoor, 1996) A rough approximation based on averaging published data is αL ≈ 0.1 L, where L is the length of flow path. Another estimate for flow lengths less than 3500 m was given by Neuman (1990) as αL ≈ 0.0175 L1.46(Delleur,1999). 2. M ATERIAL AND METHODS 2.1. Site description and field sampling Six ground-based infiltration systems were selected for sampling. These beds are: Glanshammar situated near Örebro, Tullingsås which is located in the vicinity of Strömsund, Ringamåla and Halahult located near Karlshamn, and Knivingaryd and Luvehult located near Nybro. The sampled sites are built between 1985 and 1992, which indicates at least 18 years of operation for all of them. The positions of these beds are summarized in Fig. 2. Fig. 2. Positions of the sampling sites: 1. Glanshammar, 2. Tullingsås, 3. Ringamåla and Halahult, 4. Knivingaryd and Luvehult 9 Modeling the Longevity of Infiltration System for Phosphorus Removal Sampling work was conducted by David Eveborn and Elin Elmefors between 2010-10-12 and 2010-11-05. Generally, sampling was performed in all the beds by digging a test pit in an infiltrated part of the bed and by taking one or two reference samples in a part of the bed that was so unaffected as possible. A large amount of soils (20 – 40 kg) from every sampling depth was excavated and placed in separated black garbage bags for later use. The sampling depths were: 0-5 cm, 5-15 cm, 15-30 cm, 30-60 cm and deeper than 60 cm. In order to homogenize the sample, samples from different depth were mixed in a cement mixer for 30 minutes. After homogenization, about 30 g of soil were taken out from 0-5 cm, 5-15 cm depth and from the reference soil. They were labeled and sealed into separated smaller bags and stored in a fridge (max 8℃) before the batch experiments. 2.2. Analytical work 2.2.1. Oxalate-soluble iron and aluminum From November 15 to November 24, 2010, oxalate extractions of samples were performed at the Department of Soil and Environment at Swedish University of Agricultural Sciences. The oxalate extraction used a buffer solution of ammonium oxalate and oxalic acid, which had a concentration of 0.2 M and a pH of 3. 1.00 g of soil of each sample were weighed in plastic bottles, 100 ml of water was added using a pipette to each plastic bottle with soil sample and then be shaken on a end-overend-shaker in the dark for four hours. The solutions were transferred to acid-washed centrifuge tubes and were centrifuged at 4000 rpm for 15-20 minutes. The supernatant from the centrifuge tubes were transferred to plastic. The supernatant were filtered with Acrodisc® filters and then diluted five times. All samples were submitted along with 200 ml of reference solution for analysis by means of an ICP Optima 7300 DV instrument from Perkin-Elmer (ICP-OES). The reference solutions were prepared by diluting the original oxalate solution five times in order to get the same concentration of oxalate solution as the samples. Since soil samples were more or less humid but laboratory instructions were based on air-dry samples, the results were corrected for dry weight measured for each sample. The dry weight was measured by weighing about 5 g of soil from the current samples, recording the weight, and drying them at 105 ℃ in an oven overnight. After being taken out from the oven, the samples were cooled down for about half an hour in desiccators, whereafter the weights were recorded again. 2.2.2. Batch experiment Soil samples from the 0-5 and 5-15 cm depths, and reference samples were selected from all four sampling sites (Knivingaryd, Ringamåla, Luvehult and Tullingsås). From December 8, 2010 to January 21, 2011, batch experiments were carried out in the Department of Land and Water Resources Engineering at Royal Institute of Technology. Two series of batch experiments were designed to study the phosphorus sorption isotherms (series A&B) and the effect of pH on sorption capacity (series C). The detailed design of batch experiments can be seen in Appendix III. In series A&B, a group of eight centrifuge bottles were prepared for every soil sample. 4 g of soil sample was added into each bottle, and then 10ml 0.03 M NaNO3 was added into each bottle(to get a background electrolyte of 0.01 M), and then 20 ml solution with different phosphorus concentration was added into the bottles to test the phosphorus 10 Lin Yu TRITA LWR Degree Project 12:01 sorption capacity of the soils as a function of aqueous concentration. The additions made corresponded to 0, 0.15, 0.375, 0.75, 1.125, 1.5, 2.25, and 3.75 mmol P kg-1 soil. After preparation, the samples were shaken for 5 days at room temperature. All the samples were centrifuged for 20 minutes at 3000 rpm before the next step. 5 ml of the supernatant was removed from the centrifuge bottle to a pH bottle for pH measurement immediately after centrifugation. The rest of the supernatant was added into scintillation bottle for ο-PO4 measurement by spectrophotometry (molybdate-blue method) using FIA-Aquatec®. Series C was designed to study the pH-dependent desorption of P from the samples. For this purpose, six centrifuge bottles were prepared for every soil sample. 4g soil and 10 ml 0.03 M NaNO3were added to every bottle as in series A&B. Afterwards, 20 ml solution with different concentrations of acid (as HNO3) and alkali (as NaOH) were added into the bottles. The procedures after preparation were the same as those in series A&B, i.e. shaking for 5 days, centrifugation for 20 minutes in 3000 rpm. 5 ml of the supernatant was taken out for pH measurement immediately after the centrifuge. The rest of the supernatant was filtered through an Acrodisc® PF single-use filter connected to the syringe, but the filtered solution was divided into two scintillation bottles for later measurements. The first scintillation bottle had 8 ml solution to which 267 μl ultrapure HNO3 was added. The rest of the filtered solution was put into another scintillation bottle. The pH measurements and the following process were repeated for all the supernatant. After pH measurement, all the acidified and non-acidified extracts were subjected to οPO4 measurement P by spectrophotometry using FIA-Aquatec®. Afterwards, analysis of Ca, Mg, Fe and Al was performed using ICP-OES (this analysis was performed at the Department of Geological Sciences, Stockholm University) on non-acidified bottles. 2.2.2.1 Data processing scheme of batch experiment The aim of series A&B was to study the sorption isotherm of the sampled soil. From the design details of series A&B, the processes determining sorption can be expressed as follows: (15) (16) Water Pimo + SiniSolid + PiniLiquid ⎯⎯⎯⎯ → Pimo + S1Solid + P1Liquid desorption P Solution Pimo + SiniSolid + PiniLiquid ⎯⎯⎯⎯ → Pimo + SnSolid + PnLiquid sorption The left side of both equations are the components of the sample soil, Pimo is the phosphorus in the soil which would not participate in the sorption/desorption process during the experiment; the second and third term in the left side represent the sorbed P and the initial dissolved P in the pore water of the sample soil. The first equation is the process for the No.1 sample in every group, where water is added and desorption is the governing process. The second equation is what happened in sample No.2 to sample No. 8 in every group, in which P solution was added and sorption is the main process. For the terms on the right side, S stands for sorbed phosphorus in solid phase, and P stands for dissolved phosphorus; the subscript n represents the sample number. The sorbed phosphorus on the right-hand side needs to be known to plot isotherm curves, and a mass balance is applied for this. The added phosphorus and the dissolved phosphorus after the experiment are known from experiment. The immobile phosphorus does not influence the mass balance. So the only unknown parameters are the initially sorbed phosphorus and the initially dissolved phosphate in the porewa11 Modeling the Longevity of Infiltration System for Phosphorus Removal ter of the sample. Since only 4 g of soil was added in every sample, and the dry weight of soil samples indicates a very low water content, the initially dissolved phosphorus term can be safely ignored in the following data processing. So the initial sorbed phosphorus need to be estimate in order to plot the sorption isotherms. 2.3. Parameters for Modeling 2.3.1. Flow velocity The average pore velocity would be used as one important parameter in the model, but there is not enough hydrogeological data to solve the flow equation. So a simplified flow velocity is assumed on the basis of the infiltration system design criterion, and the soil in the model is assumed to be both homogeneous and isotropic. The sampled sites are designed for the sewage treatment of one household with 5 persons. The estimated inflow into the infiltration bed is 150 – 200 L/D for one person, so the total inflow per day is between 750 L and 1000 L (0.75 – 1 m3). In the design criteria EC/EWPCA (1990), the area of the infiltration system is 5 m2 per person, so the area of the whole infiltration bed is about 25 m2. The inflow and outflow of the system is the same since the system is assumed to be in a water balance, so the estimated mean pore velocity should be between 0.03 and 0.04 m/D throughout the whole infiltration bed. 2.3.2. Retardation factor The basic Freundlich sorption isotherm is chosen to study the relationship between the dissolved P concentration and phosphate sorption of the solid phase. The basic Freundlich is written as below, (17) S = KF × C I , where S = sorbed phosphate in equilibrium state, MM-1 KF = coefficient, dimensionless C = equilibrium phosphate concentration I = coefficient, dimensionless Incorporating the kinetic component into the Freundlich equation requires a solution to the following first order differential equation: ∂S = β (KF C I − S ) (18) ∂t , where β = kinetic rate constant for the reaction, L-1 Cs in equation (8) can be considered of including two parts, the original P in soil matrix and the sorbed P, which is S in the Freundlich equation. So (19) Cs = Cini + S = Cini + K F × C I As Cini does not change with time, ∂Cs/∂t actually equals with ∂S/∂t, 12 Lin Yu TRITA LWR Degree Project 12:01 ∂Cs ∂S ∂C = = K F × I × C I −1 × ∂t ∂t (20) ∂t Substitute equation (19) with equation (8). One gets, ρb ∂C ∂C ∂ 2C K F IC I −1 ) = −v + DL 2 θ ∂t ∂x ∂x (21) ρ Set R = 1 + b K F IC I −1 , thus the final transport equation in this study θ (1 + becomes: ∂C v ∂C DL ∂ 2C =− + R ∂x R ∂x 2 (22) ∂t ρ , where R = 1 + b K F IC I −1 . θ 2.3.3. Hydrogeological Parameters In equation (21), ρb (bulk density), θ (volumetric water content) and v (Darcy’s flux) are required to solve the equation. The bulk (dry) density is the ratio of the solid phase of the soil to its total volume and can be determined from the knowledge of dry weight (Ms), solid particle density (ρs) and porosity (n). The equation is: ρb = (23) , where V = Mt Ms 1 × ρs n Ms ρs × 1 and Mt is the total mass of the soil, then the volun metric water content can also be obtained, (24) θ= Mt − Ms V Darcy’s flux represents the real transport velocity of the solute in soil, with the definition, (25) v = ux θ Where ux is the average pore velocity; it is already estimated in section 2.3.1. The dry weight of the soil had already been measured (Appendix I), and the particle density is well accepted to be about 2.4 kg/dm3. The porosity would be estimated based on soil texture using empirical data (See Appendix IV). A simplified linear pedofunction was used in the calculation process. The dipersion coefficient was approximated as αL ≈ 0.1 L, where the flow path length L was assumed to be the length of the soil column in the model. 13 Modeling the Longevity of Infiltration System for Phosphorus Removal 2.4. Numerical solution scheme Forward difference methods were applied in this study to solve equation (21) numerically. After assuming that the ADE had a rectangle domain R = {(x, t): 0≤x≤a, 0≤t≤b}, R was subdivided into n-1 by m-1 rectangles with sides ∆x=h, ∆t=k, as shown in Fig. 3. C(x,t) would be approximated at grid points in successive rows {C(xi, tj): i = 1,2,…,m, j = 1,2,…,n}. The length of the time step (∆t) is of importance to the stability of the numerical solution scheme. The timestep must satisfy ∆t ≤ (∆x)2/2DL (Mathews and Fink, 2003). The sorption process in this study was assumed to be finished instantly in every grid. Therefore the time step must be smaller than both advective time and dispersive time during one grid (Parkhurst and Appelo, 1999). The time step can slso be simplified just as ∆t ≤ ∆x/v (Notodarmojo et al., 1992). The grid point C(xi, tj) is written as Ci,j in the following deduction. (26) ∂C Ci , j +1 − Ci , j = + ο (k ) ∂t k ∂C Ci , j − Ci −1, j = + ο ( h) h (27) ∂x ∂ 2C Ci +1, j − 2Ci , j + Ci −1, j = + ο (h 2 ) 2 2 ∂ x h (28) Equation (21) was substituted with equations (26) - (28), and the terms ο(k), ο(h) and o(h2) were dropped: Ci , j +1 − Ci , j (29) k =− v ⎡ Ci , j − Ci −1, j ⎤ DL ⎡ Ci +1, j − 2Ci , j + Ci −1, j ⎤ ⎥+ R ⎢ ⎥ R ⎢⎣ h h2 ⎦ ⎣ ⎦ Fig. 3. The grid for solving equation (21) over domain rectangular 14 Lin Yu TRITA LWR Degree Project 12:01 ρb K IC I −1 . In order to avoid confuθ F ρ sion in notations, set R = 1 + UCu-1, where U = b K F I , u = I in exθ As assumed before, here R = 1 + pression R. One will get: (30) (1 + UC i, j u −1 ) Ci , j +1 − Ci , j k = −v Ci , j − Ci −1, j h + DL Ci +1, j − 2Ci , j + Ci −1, j h2 Rearrange terms, the new function can be used for the computation: kD L kv 2 kD L ⎞ vk kD L ⎛ C i , j +1 (1 + UC i , j u −1 ) = UC i , j u + ⎜ 1 − − ⎟ C i , j + ( + 2 ) C i −1, j + 2 C i +1, j 2 h h ⎠ h h h ⎝ (31) 2.5. Model description Conceptual model for the column study: A simplified model was built to study the longevity from using a column study which aims at simulating the real infiltration system. Many researchers used such column experiments as tools to predict the sorption capacity and longevity expect of sorbent materials (Heistad et al., 2006; Renman and Renman, 2010). Since the boundary condition of the model is not certain, the depth of the model is set to 2 m in order to weaken the impact of unknown boundary condition in the numerical solution. The soil in the model was assumed to be totally homogenous and isotropic and the same as in other real column studies. Water flow is assumed to be unsaturated flow and constant continuous inflow. The flow rate is calculated from the Swedish criteria for infiltration systems. The dominant process in the model would be the solute transport process; however, retardation would play a more important role than advection and dispersion in determining the longevity in the model. The discretization of the domain is setting distance step to 0.01 m and the time step to 0.1 day. The structure of the model for simulating column experiment is shown in Fig. 4 (Matlab codes of the model see Appendix VI). Fig. 4. Conceptual model for the soil column 15 Modeling the Longevity of Infiltration System for Phosphorus Removal 2.5.1. Modeling tools 2.5.1.1 Matlab MATLAB® is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numerical computation. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran. MATLAB was developed by Cleve Moler, the chairman of the computer-science department at the University of New Mexico in the late 1970s. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded MathWorks in 1984 to continue its development. MATLAB was first adopted by researchers and practitioners in control engineering, Little's specialty, but quickly spread to many other domains. It is now also used in education, in particular the teaching of linear algebra and numerical analysis, and is popular amongst scientists involved in image processing (Wikipedia). 2.5.1.2 Visual MINTEQ Visual MINTEQ is a freeware chemical equilibrium model for the calculation of metal speciation, solubility equilibria, sorption etc. for natural waters. It combines state-of-the-art descriptions of sorption and complexation reactions with easy-to-use menus and options for importing and exporting data from/to Excel. The latest version of Visual MINTEQ (ver. 3.0, Jon Petter Gustafsson, 2011) was used in this study to process the chemical speciation of the extracts from the pH-dependence experiments. The solution activities were calculated from the output of Visual MINTEQ and compared to the solubility constants from the literature. 2.5.2. Modeling scenarios Basic Scenario: three basic scenarios were applied for the preliminary prediction of longevity of soil column system with soil from three sampling sites. Parameters input are derived from the raw experiment data, the modeling time period was set to 5000 days. A reference phosphorus concentration of 0.015 mg/L all along the column is set to be the initial condition at starting time. A constant inflow of 5mg/L at starting point is accepted as one boundary condition; as for the boundary condition at depth equals 2 meters, a slow linear increasing is assumed in the modeling period, and the concentration would increase from the reference concentration till the critical concentration, 1 mg/L. Table 2 shows the inputs for Basic Scenario. In order to get shorter running time for the sensitivity analysis and better comparison Fig.s, a new set of input was used as the basis for the scenarios. With U = 0.03 m/D, θ = 0.12 kg/m3, n = 0.40, Kf = 3.0213 and I = 0.5968. The modeling time was set to 300 days, and it is refered as Scenario 0 in the following text. 16 Lin Yu TRITA LWR Degree Project 12:01 Table 2 Model Setting for Basic Scenario, ux is the average pore velocity, θ is the volumetric water content, n is the porosity, ρb is the bulk density, Kf and I are coefficients in equation (12) 3 3 ux(m/D) θ(kg/m ) n ρb( kg/m ) Kf Kn 0.03 0.12035 0.3984 1.5642 10 Lu 0.03 0.13375 0.3932 1.5901 Ri 0.03 0.12045 0.3965 1.5688 IC C(x,0)=c1=0.015 mg/L BC C(0,t)=c2=5 mg/L; C(2,t)= c1+t*(1-c1)/2*5000 I 1.9201 0.4866 10 2.2282 0.3423 10 1.8278 0.5968 Scenario 1: this scenario was created to study the influence of modeling time. The setting of this model was the same as Scenario 0, but with a modeling time of 5000 days as comparison. Scenario 2: this scenario was set up to study the influence of P sorption capacity of the soil. Two sub-scenarios were set to study the impacts of Kf and I from Freundlich isotherm separately. In sub-scenario 2.1, the value of Kf was entered as 0.5, 1, 2, 3 and 5, and the rest of the inputs were the same as Scenario 0. In sub-scenario 2.2, the value of I was input as 0.25, 0.35, 0.45, 0.55 and 0.7, and the rest of inputs were the same as Scenario 0. Scenario 3: this scenario was built to study the influence of inflow P concentration and background P concentration. It was also built on Scenario 0 with the modeling time of 1000 days, and contains two subscenarios. Sub-scenario 3.1 has a changing inflow P concentrations of 3 mg/L, 5 mg/L, 8 mg/L and 10 mg/L; sub-scenario 3.2 has various background concentrations of 0.001 mg/L, 0.015 mg/L, 0.05 mg/L and 0.1 mg/L. Scenario 4: this scenario was built to study the sensitivity of flow velocity to the P concentration. It was built on Scenario 0 with 1000 days as modleing time, with different flow velocities: 0.003 m/D, 0.01 m/D, 0.02 m/D, 0.03 m/D and 0.05 m/D. Scenario 5: this scenario was built to study the model reactions to the change of volumetric water content under two different flow velocities. It was built on the basis of Scenario 0 under 1000 days’ modeling time, with two different flow velocities: 0.01 m/D and 0.03 m/D, and three volumetric water contents: 0.08, 0.12 and 0.2. 3. R ESULTS 3.1. Oxalate extraction Appendix II shows the oxalate-soluble phosphorus concentrations of all sampling sites. All the reference samples from the six sampling sites had lower oxalate-soluble phosphorus than their correlated surface soil. However, in Glanshammar, the oxalate-soluble phosphorus was only slightly less than the phosphorus of surface soil in the infiltration bed; it might indicate that the reference plot has been subject to P from the infiltration bed. Oxalate-soluble phosphorus from the surface horizons (0-5, 5-15 cm) of most sites had a value of around 0.25 mg/g. Meanwhile, in Luvehult, the oxalate soluble P in 0-5 cm and 5-15 cm soil were 1.14 mg/g and 1.04 mg/g, and in Tullingsås the oxalate-soluble P in 5-15 cm was 7.07 mg/g (Appendix II). No obvious difference between the 0.5 17 Modeling the Longevity of Infiltration System for Phosphorus Removal and 5-15 cm horizons could be observed in the Luvehult soil. However, the P concentration in the reference sample was also quite low, and one can conclude that the high P in the surface horizons are probably because of the high P level in sewage or exhausting P retention ability in the soil. For all the sites, there were obvious positive correlations between P and Al, as well as between P and Fe. But the relationship between P and Al (r2=0.93) was much stronger than that of P and Fe (r2=0.77) The dry weights are presented in Appendix I. The horizon 0-5 cm in site Tullingsås had a very low dry weight of 0.332 g/g, which indicates quite high water content in that layer. The rest of the results were in the normal range of mineral soils. Fig. 5. Relation between oxalate-soluble P and oxalate-soluble Al Fig. 6. Relation between oxalate-soluble P and oxalate-soluble Fe 18 Lin Yu TRITA LWR Degree Project 12:01 3.2. Batch Experiments 3.2.1. Phosphorus sorption experiments Four sampling sites were selected for the batch experiments; they are Knivingaryd, Ringamåla, Luvehult and Tullingsås. Due to the high organic content and remnant vegetation in the soil from Tullingsås, the filtering step failed during the experiments, therefore the data from Tullingsås were not used anymore. As shown in Appendix III, soil from every sample was added into 8 bottles for isotherm experiments, which can be used to determine the phosphorus sorption capacity at different concentrations of dissolved phosphate. As tested by Kafkafi et al. (1967) the plotting of isotherms from sorption data is appropriate where the sorbing surfaces are on a prepared pure mineral material or a virgin soil. Barrow (1978) discusses the need to consider P already present in the soil when fitting the basic Freundlich isotherm to experimental sorption data, suggesting an extra term in the isotherm: S =S +S = K CI ini sorb f (32) , where S is the total sorbed phosphorus in the soil, it is also S nSolid in equation (15) and (16). Sini is the already sorbed phosphorus in the soil sample and Ssorb is the newly sorbed phosphorus during the experiment. In the data processing, Sini needs to be estimated to plot the Freundlich isotherms. An estimation of the quantity of phosphorus in the solid phase is needed to plot the Freundlich isotherm curve. For each group of test, to get an initial value of the solid phase phosphorus concentration in the added soil sample, log-linear regression was run by the means of trial and error using Microsoft Excel as first estimation. Then optimization was made by applying log-linear regression of all three groups of data (reference soil, horizon 0-5 cm and horizon 5-15 cm) in a same sampling site. All the three estimated Sini of reference soil, horizon 0-5 cm and horizon 5-15 cm would change at the same time, in the extent of ±20% of the first estimation value. A new determining number was used to decide the best estimated Sini in the concern of the whole sampling site; it was the sum of the three r2 (from the linear regressions of reference soil, horizon 0-5 cm and horizon 5-15 cm) and three times r2 from the linear regression of the whole sampling site. Matlab was used to execute the optimization. Data from samples with no P addition was excluded in this step since the process in these was desorption not sorption. The results are shown in Fig. 7. When the estimated phosphorus concentration in the solid phase and the oxalate soluble P were compared, a quite good linear fit (r2 = 0.97) was obtained (Fig. 8). Generally, all the soils sorbed more phosphorus while supplied with higher P concentration in water phase; for the highest added P concentration in this study (0.5 mM), no obvious evidence of sorption ability exhaustion could be found. 19 Modeling the Longevity of Infiltration System for Phosphorus Removal (a) (b) Fig. 7. Phosphorus sorption isotherms of sampling sites: (a) Knivingaryd; (b) Luvehult; (c) Ringamåla. (c) As for the sorption isotherms, all the 9 groups of tests turned out to get a quite good fit after first estimation, 4 groups had r2 of 0.99, 3 groups had r2 of 0.98 and the other 2 groups had r2 of 0.96. While the fit for every site were also quite good after adjusting, with r2 = 0.979 in Knivingaryd, r2 = 0.928 in Ringamåla and r2 = 0.969 in Luvehult. However, from the shape of regression curve, it is observed that the curve for reference site has slightly deviation compared with curves for soils from infiltration beds. And the result of log-linear regression of all the three sites gave a really unsatisfying r2 of 0.699. It implies that in fact the sorption of phosphorus is also influenced not only by the solution concentration of phosphorus, but also by many other factors, such as concentration of Ca, Fe and Al and so on. For soils in the same infiltration beds, the other factors have similar or same impact on the P sorption, but in the correlated reference site, the influence of those other factors is not the same as that in infiltration bed, and bigger difference can be observed among different sites (Fig. 7). (a) (b) Fig. 8. Relation between estimated initial solid P (Sini) and oxalate soluble P. In (a), x axis stands for Pox and y axis stands for Sini, both in mg/g; in (b) y axis stands for the sampling sites. 20 Lin Yu TRITA LWR Degree Project 12:01 It is interesting to mention another researcher’s description about the oxalate-extractable P content of the soil. Lookman et al. (1995) describes the oxalate-extractable P as: Pox = Pfast + Pslow, where Pox is oxalateextractable P, Pfast is P pool for the fast desorption and Pslow is the P pool for slow reaction. However, it is obvious in this study that the estimated Sini is much smaller than the Pox, which might imply that 5 days’ shaking in this study is not long enough for the soil sample to complete the slow reaction, especially under the consideration that these soils were taken from infiltration beds which have had a service time of longer than 18 years. Noticing that 5 days’ shaking time is not enough for the slow action of sorption/desorption, it is necessary to use the sorption kinetics in the modeling rather than the isotherm, given the possibility that the sorption capacity might also increase during the process because the accumulation of metal (hydr)oxides. If the fast step of sorption/desorption is an instant reaction, so the estimated Sini here might contain all the fast reaction P pool and a very small part of the slow reaction P pool, which is small enough here to be neglected. So the isotherm obtained in this study is just for the fast reaction of sorption. Noticing the different sizes of the slow reaction P pool from Fig. 8(b), relations between the metal concentration and slow reaction P pool were plotted to see the correlation. Results (Fig. 9) give a stronger correlation with Fe than Al, while in Fig. 5 and Fig. 6, Al has stronger correlation with oxalate-soluble P. It can be concluded that Al would influence more on the fast reaction and Fe would impact more on the slow reaction of sorption/desorption of P. Supportive information for the necessity of including sorption/desorption kinetics in the modeling is presented above. If the estimated Sini value is returned to the isotherm obtained in this study, to calculate the initial P concentration in the dissolved phase, an unreasonably small value would be returned. However, if the measured oxalatesoluble P is used to calculate the initial P concentration in the dissolved phase, the results turn to be much realistic except for the results for Lu (Table 3). From the returned value of initially dissolved in the Luvehult site, one can make a guess that the sewage P concentration there is really high. At the same time, due to the relative high metal (hydr)oxide concentration in site Luvehult, it is reasonable to point out that the basic Freundlich isotherm obtained in this study is not applicable to the Luvehult site due to high metal concentrations and possibly other factors. Use of other approaches (such as the Extended Freundlich isotherm with kinetics), including concentrations of metal (hydr)oxides should be studied for site Luvehult P mg/g Fig. 9. Relation between slow P pool and oxalate-soluble Al & Fe. 21 M Modeling the Longevity L of In nfiltration Systtem for Phosp phorus Removval Table le 3 Return rned value of o initial P concentratio c ion in liquid d phasee returned by Sini returned byy Pox PiniLiquid PiniLiquid mgg/L mg/L Kn ref 0.0836 0.351 Kn 0-5 5 0.122 4.341 Kn 5-15 0.120 4.082 Lu ref 0.000488 8 0.076 Lu 0-5 0.712 266.226 Lu 5-15 5 0.780 201.02 Ri ref 0.676 0.737 Ri 0-5 0.558 7.377 Ri 5-15 5 0.751 7.100 3.2.2. pHdep pendence expe periments Phosph horus desorption was fouund to be verry sensitive tto pH (Fig. 10). 1 In veryy acid envirronments (p pH<4.0), muuch phospho orus would be desorbeed; while pH H stays from 4.0 to its no ormal pH vallue (5.2 to 6..1), less butt similar amount of phosp phorus wouldd be desorbedd. However, ded sorption n increases aggain at higher pH; a smalll rise in pH frrom the norm mal pH con ndition causees P desorptiion to increaase dramaticaally. Soils fro om differen nt sites tendeed to have different sensittivity to pH cchange. In RinR gamåla and Knivinggaryd, desorp ption at loweer pH was o obviously muuch higher than at otheer pH condiitions; but in n Luvehult ddesorption was w much higher h when alkali a was add ded. (a) (b) Fig. g. 10. pH an nd dissolved d phosphorrus con ncentration in pH depen ndence test: (a) Knivingaryd K d; (b) Luvehult; L (c) Ringamåla. R (c) 22 Lin Yu TRITA LWR Degree Project 12:01 Wang et al. (2005) has also got similar results on the relation between pH and phosphorus concentration during desorption process. Meanwhile the influence of pH on sorption process is also different from that of desorption. Similar conclusion is also drawn by Mohsen Jalali et al. (2011) that H+ contribute most to the release of phosphorus from soil. As for now, no general understanding of sorption/desorption processes is accepted by the academic field. It is still considered to be a mix of many processes, such as “deposition”, “fixation”, “pricipitation” and “solidphase diffusion”. It is believe that the adsorption and desorption capacity of P with different sediments is a rather complex consequence of multiple factors and their interactions, e.g., pH value, electrical conductivity, mineral or metal oxide type, particle size in related to the total surface area, organic matter, etc (Wang and Li, 2010). Indicated by this study and study of Wang et al. (2005), the influence of pH was more probably on fast reaction of sorption/desorption, but due to the lack of experiment data and well-fit kinetics, it is still unknown if pH would also impact the slow reaction of sorption/desorption. The effort of trying to plot desorption isotherm with Freundlich isotherm has also turned out to be unsatisfying in this study. The hypothesis was adopted that sorption/desorption was totally reversible before the plotting. Estimated values of initial solid phase P from isotherm tests (Sini) were used at first, but the data based on those values had really bad fitting. The r2 for Kn was 0.865, for Lu was 0.938 and for Ri was 0.742, which are all worse than the fits for the sorption isotherms. The r2 for all the three sites taken together was only 0.01, which can be considered as an indication of no correlation. This result indicates that desorption process is not a totally reversible process of sorption, and possibly that the Freundlich isotherm is not the best model for the isotherm of desorption. New isotherms for desorption should be applied. Many researchers (Hooda et al., 2000; Lookman et al., 1995; Jalali and Varasteh, 2011) have suggested several isotherms and kinetics for the desorption of phosphorus in soils. (a) (b) Fig. 11. Relations between desorbed phosphorus and Al, Ca, Mg concentration in pH dependence experiments: (a) Knivingaryd; (b) Luvehult; (c) Ringamåla. (c) 23 Modeling the Longevity of Infiltration System for Phosphorus Removal (a) (b) Fig. 12. Relations between pH and Ca, Mg concentration in pH dependencen experiments: (a) Knivingaryd; (b) Luvehult; (c) Ringamåla. (c) Fig. 11 shows the relationships between desorbed phosphorus and Al, Ca and Fe concentration. The solution concentration of Al follows a good linear correlation with desorbed P in all the three sites (in site Luvehult two bad points were excluded), the linear r2 for Knivingaryd, Luvehult and Ringamåla are 0.93, 0.90 and 0.87, but no apparent relations between Ca and P, Fe and P could be found. Fig. 12 shows a good exponential correlation between pH and Ca & Mg concentration, but the mechanisms among pH, metal (hydro) oxides and P sorption are still unknown from these simple results. Fig. 13. Solubility constants and heat of reaction for Ca phosphates in this study 24 Lin Yu TRITA LWR Degree Project 12:01 3.2.3. Chemical Speciation Results Chemical speciation modeling was made using Visual MINTEQ (ver. 3.0, Jon Petter Gustafsson, 2010). Of all the input concentrations to Visual MINTEQ, Na+ and NO3- were calculated from the experiment design details, and the rest are measured results from lab work. Four calcium phosphates are studied as potential precipitates, which are amorphous calcium phosphate, ACP ((Ca)3(PO4)2(s)), hydroxyapatite, Hap (Ca5(PO4)3OH(s)), octacalcium phosphate, OCP (Ca4H(PO4)3(s)), monetite, DCP (CaHPO4(s)) and brushite, DCPD (CaHPO4·2H2O). The solubility constants of them were taken from one previous study of Kong (2009), which can be seen in Fig. 13. The results of chemical speciation for the calcium phosphates in the pH dependence extracts are shown in Fig. 14. As is seen in the Fig. 14, only HAp becomes supersaturated as pH increases to 6 or higher. It is consistent with the results from Kong (2009), while they had got more samples supersaturated with respect to HAp than in this study, as well as samples that were close saturation with respect to ACP. However their extracts did not appear to precipitate as the model results indicate. The present study shows that calcium phosphate probably did not control the solubility of P, as the solubility lines were much higher than the data from the samples. -24 -45 -26 ACP1 -28 -50 HAP ACP2 -30 -32 -55 -34 -36 -60 -38 -40 -65 -42 -44 3 3.5 4 4.5 5 pH 5.5 6 6.5 -70 7 -40 3.5 4 4.5 5 pH 5.5 6 6.5 7 6 6.5 7 -12 -45 -13 OCP -50 -14 -55 -15 -60 -16 -65 -17 -70 -18 -75 -19 -80 -20 -85 3 3 3.5 4 4.5 5 pH 5.5 6 6.5 -21 7 DCPD DCP 3 3.5 4 4.5 5 pH 5.5 Fig. 14. Solubility diagrams for soils from horizons 0-5 cm and 5-15 cm of Knivingaryd, Luvehult and Ringamåla. The red + stands for results from Knivingaryd, the blue circles stand for results from Luvehult and the cyan stars stand for results from Ringamåla. Points above the lines represent supersaturation. 25 Modeling the Longevity of Infiltration System for Phosphorus Removal 3.3. Modeling results 3.3.1. Calculated Model Inputs Some of the unknown inputs of the model were derived from the experiment data; sorption data, soil dry weight and soil texture data were used in this study to calculate the inputs needed for model. After optimization of the initial solid phosphorus concentration, the returned Kf and I values for Knivingaryd, Luvehult and Ringamåla were calculated from sorption data, they were 101.9201, 102.2282, 101.8278 and 0.4866, 0.3423, 0.5968. The I values in Kn and Ri were higher compared with related studies on Freundlich isotherms; many researchers have obtained I values around 0.35 (Gustafsson, 2011). Since limited soil data were measured in the study sites, bulk density and volumetric water content can be only obtained in the 0-5 cm and 5-15 cm soil horizons. So in the prediction of longevity for the studied sites, the average value of the two surface horizons is used as input for the whole modeling column. The bulk densities of Kn, Lu and Ri were 1.5642, 1.5901 and 1.56885 g/cm3, and the volumetric water content of Kn, Lu and Ri were 0.12035, 0.13375 and 0.12045 g/cm3. 3.3.2. Longevity prediction of Kn, Lu and Ri Based on the input from Basic Scenario, the concentration of soil column at a depth of 1 m is plot as Fig. 15. An obvious retardation can be noticed in all the three soil columns, while when advective/dispersive transport reaches the studying depth, the concentration of phosphorus would increase dramatically. In the soil column from Kn, the P concentration would reach 1 mg/L at 1703th day, and on 2531th day, the concentration would reach the inflow concentration (5 mg/L) of the system. For the soil column from Ri and Lu, the time to reach the critical concentration and max concentration were 1674th day & 2709th day and 2575th day & 3673th day. By using the definition of longevity in this study, the longevity of the three soil columns were 1703 days, 1674 days and 2575 days. The exhaustion time of the three soil columns under inflow of 5 mg/L were 2531 days, 2709 days and 3673 days. 6 concentration: mg/L 5 4 3 Lu 2 1 0 Ri 0 500 Kn 1000 1500 2000 2500 3000 time: Day 3500 4000 4500 5000 Fig. 15. Results of Basic Scenario – the estimation of longevity for soil column in three sampling sites 26 Lin Yu TRITA LWR Degree Project 12:01 6 6 5 5 concentration: mg/L concentration: mg/L 3.3.3. Effect of the Modeling time 4 3 2 1 0 4 3 2 1 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 0 50 100 150 time: Day time:Day (a) (b) 200 250 300 Fig. 16. Modeling results of Scenario 1 – Different modeling time: (a) modeling time = 5000 days; (b) modeling time = 300 days The preliminary modeling time in Basic Scenario was set to 5000 days. The prediction from basic scenarios shows that, during most of the modeling period, the P concentration at depth of 1 m is as high as the inflow P concentration. Variations of modeling time were made to study the impacts on the concentration at 1 m depth. Two sub-scenarios were run on the basis of Scenario 0, while the modeling times in the two scenarios were 5000 days and 300 days, separately. The results can be seen in Fig. 16. By plotting the time required to reach the critical concentration, it is found that the concentration curves are almost the same compared to the Scenario 0. However, the surface curves for all the modeling time and depth are quite different in these three scenarios. The reason for this is the discretization scheme in the numerical solution. For the finite different method, the computation of every grid point depends on the neighboring grids; while in this study, in order to keep the stability of the numerical solution, a smaller time step was required during the discretization. It caused the model to be less sensitive in the change of modeling time. Another reason is that, the study depth is the middle point of the whole modeling depth, small change in the boundary conditions would be weaken because of too much grid points between the study spot and the boundary. 3.3.4. Effect of the Soil Sorption Capacity In order to study the impact of sorption capacity, a new scenario was set up with the same soil properties for all three sites but remains their own phosphorus sorption capacity, and the modeling time was set to be 300 days for a better visual effect. As Fig. 17 shows, with the same soil properties, the soil column from Ri has the longest life expectancy and Lu has the shortest, which is the same as the Basic Scenario suggests. By comparing the longevity of this scenario with Basic Scenario, it is noticed that both give similar results. This demonstrates the similarity of soil conditions of the three sampling sites. 27 Modeling the Longevity of Infiltration System for Phosphorus Removal 6 5 concentration: mg/L Kn 4 Lu 3 Ri 2 1 0 0 50 100 150 time: Day 200 250 300 Fig. 17. Modeling results for the P sorption capacity comparison It can also be easily concluded from Fig. 18 that a higher I value gives a longer longevity of the soil column, and another curious appearance is that a higher I value also extends the sorption time of the soil column. While from the Fig. its appearance is the slope of the curve decreases as I value increases, but in Fig. 18(a), since the change of Kf value is really small in this sub-scenario, no obvious change in sorption time can be observed. One extra test was done by varying the Kf in the range of real situation (101.5, 101.8, 102), the result showed that the increasing Kf value would also cause a longer sorption time, but the rise of sorption time is much less comparing to the rise of Kf. 6 5 concentration: mg/L Kf=0.5 4 Kf=1 Kf=2 3 Kf=3 2 Kf=5 1 0 0 50 100 150 time: Day 200 250 200 250 300 (a) 6 5 concentration: mg/L I=0.25 4 I=0.35 I=0.45 3 I=0.55 I=0.7 2 1 0 0 50 100 150 time: Day 300 (b) Fig. 18. Modeling results of Scenario 2 – Different P sorption capacity: (a) sub-scenario 2.1; (b) sub-scenario 2.2. 28 Lin Yu TRITA LWR Degree Project 12:01 The sorption capacity is the most import factor to evaluate the filter material and researchers normally are using batch experiments and column experiments to evaluate the PSC of filter materials with sorption isotherms. However, it is pointed out by Cucarella, V. and Renman, G. (2009) that forms and amounts of filter materials, material to solution ratio, intial P concentration and contact time, agitation & temperature would all have influences on the PSC results from batch experiments. Concerning this study, it could also be possible the PSC achieved in this study is overestimated comparing to real filed data, or even to column experiment data. 3.3.5. Effect of inflow concentration and background concentration Two sub-scenarios were run to test the sensitivity to the change of inflow concentrations and background concentrations. Results are shown in Fig. 19. The background concentration of the model, which is also the initial condition in the ADE equation, has a very low influence on the concentration change and life expectancy. The model is much more sensitive to the change of inflow P concentration. As the inflow P concentration decreases; both the time for the soil column to reach the critical concentration and the time for the soil column to reach exhaustion would increase. In reality, the sewage phosphorus concentration can be a key factor for the sorption of the infiltration beds and the longevity, also changing inflow concentration may be expected in real infiltration systems. But unfortunately, for normal household on-site infiltration systems, it is expected to have an intermittent sewage inflow. The situation could be that, during peak hours such as morning or dinner time, most sewage with a high P concentration would go into the infiltration system, and for most time of the day, little or no sewage would be emitted, with relatively lower concentration of phosphorus also. Both flow condtions and sorption mechanisms could change due to the complicated sewage inflow, and more detailed modeling should be done to cope with the real situation. 12 6 10 5 8 concentration: mg/L concentration: mg/L C2=10 mg/L C2=8 mg/L 6 C2=5 mg/L 4 2 0 50 100 150 time: Day 3 2 1 C2=3 mg/L 0 4 200 250 0 300 (a) 0 50 100 150 time: Day 200 250 300 (b) Fig. 19. Modeling results of Scenario 3 – Different inflow P concentration and background P concentration: (a) sub-scenario 3.1; (b) sub-scenario 3.2, where yellow line for c2 = 0.001 mg/L, red line for c2 = 0.015 mg/L, blue line for c2 = 0.05 mg/L and cyan line for c2 = 0.1 mg/L. 29 Modeling the Longevity of Infiltration System for Phosphorus Removal 6 5 concentration: mg/L U=0.05 m/D 4 U=0.03 m/D U=0.02 m/D 3 U=0.01 m/D 2 U=0.003 m/D 1 0 0 100 200 300 400 500 600 time: Day 700 800 900 1000 Fig. 20. Modeling results of Scenario 4 – Different flow velocity (average pore velocity) 3.3.6. Sensitivity analysis of soil properties Flow velocity: the average flow velocity was estimated by the amount of sewage emission and infiltration bed areas from design criteria. It affected the dispersion and advection at the same time in this study and can be of considerable interest in the sensitivity analysis. Scenario 4 was set up on the basis of Scenario 0, with changing velocities 0.003 m/D, 0.01 m/D, 0.02 m/D 0.03 m/D and 0.05 m/D. The results are shown in Fig. 20. Higher velocity gives a shorter retardation period for the soil to start sorption, and at the same time shorter time for the soil to reach sorption capacity. When velocity decreases, the life expectancy of the soil column increases, and the increase is larger with decreasing velocity. In other words, the model is more sensitive when the flow velocity is lower. It is noticed that the above scenario is built on very small volumetric water content; it would somehow amplify the effect of velocity change since in the model the flux velocity is applied for advective transport, rather than the average pore velocity. The sensitivity of volumetric water content is also interesting in this study, since it is both related with retardation and advection in transport equation. Scenario 5 is developed with various volumetric water content and velocity, with results shown in Fig. 21. The smaller volumetric water content can contribute to a decrease of the slope of the concentration curve, which means that it can increase the longevity of the soil column and at the same time decrease the sorption time of the system. However, from the above Fig., the increase of longevity seems to be affteced by other factors such as velocity in Fig. 21, and other factors may also have influence on the amount of longevity change. The last input of soil property in the model is the bulk density. From equation (21) it is easy to see that the bulk density has the same sensitivity as the volumetric water content, but with an opposite direction of change. 30 Lin Yu TRITA LWR Degree Project 12:01 6 concentration: mg/L 5 4 3 Blue: U=0.03, theta=0.08 Red: U=0.03, theta=0.12 Cyan: U=0.03, theta=0.2 Green: U=0.01,theta=0.08 Yellow: U=0.01, theta=0.12 Black: U=0.01, theta=0.2 2 1 0 0 100 200 300 400 500 600 time: Day 700 800 900 1000 Fig. 21. Modeling results of Scenario 5 – Different volumetric water contents under two flow velocities It needs to be pointed out that the flow velocity in this modeling study is quite simplified due to the lack of data for soil properties and limited time. Even for the estimation of bulk density and volumetric water content, simplified equations and methods were applied. Theoretically the better way for the required soil properties in the model should be direct measurement, and the input of flow velocity should be based on the real situation as mentioned in last section, and also based on flow equations, where even more details of flow conditions could be used for the estimation of dispersion coefficient in the Advection-Dispersion equation. 3.3.7. Sorption capacity study and sorption velocity 5 5 4.5 4.5 4 4 t=1703 D 3.5 3 concentration: mg/L concentration: mg/L 3.5 t=2531 D 2.5 2 1.5 2.5 t=3673 D 2 1.5 1 1 0.5 0.5 0 t=2575 D 3 0 0.2 0.4 0.6 0.8 1 1.2 depth: m 1.4 1.6 1.8 0 2 (a) 0 0.2 0.4 0.6 0.8 1 1.2 depth: m 1.4 1.6 1.8 2 (b) 5 Fig. 22. Soil column P concentration distribution, red lines represent the time for depth = 1 m to reach 1 mg/L, the blue lines represent the time for depth = 1 m to reach inflow concentration: (a) Knivingaryd; (b) Luvehult; (c) Ringamåla. 4.5 t=1674 D 4 concentration: mg/L 3.5 3 t=2709 D 2.5 2 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 depth: m 1.4 1.6 1.8 2 (c) 31 Modeling the Longevity of Infiltration System for Phosphorus Removal It is well accepted that the sorption capacity can not be fully predicted based on the Freundlich isotherm. As in this study, the sorption capacity of the soil can be determined by the coefficient Kf and I in equation (17), and the only available outcome based on those coefficients is the maximum P sorption under a certain inflow concentration. Compared to the phosphorus sorption capacity (Spsc) used in equation (1), the maximum P sorption under a certain inflow is a much reasonable value to predict the longevity of sorbents/infiltration beds using that method. However, the time to reach maximum P sorption and the time to reach critical P concentration are also different. As shown in Fig. 17, the time for Lu to reach the critical concentraton at 1 m depth is 2575 days, and the time for Lu to reach its exhaustion at 5 mg/L inflow P concentration is 3673 days. In fact the sorbed phosphorus in the soil column can be calculated based on the result of the model if the size and density of the soil column is known. 100 (33) Stotal = m × ∑ K f C ( x, t ) I n =1 Where Stotal is the sorbed quantity of phosphorus, m is the unit mass for a single model cell shown in Fig. 4, and t here is a fixed number. Since the column soil with 1 m depth is divided into 100 cells in this study, the accumulated number is set to be 100. The calculated sorbed phosphorus quantity for soil from sites Kn, Lu and Ri when they reach the critical concentration are 0.177, 0.288 and 0.168 mg/g, while the maximum sorption of Kn, Lu and Ri are 0.182, 0.293 and 0.176 mg/g separately. It is obvious that after the concentration reaches critical concentration, actually not much P would be sorbed into the soil column in all the sites, which can be easier to infer from Fig. 22. 300 Lu 250 sorption: ug/kg 200 150 Kn 100 Ri 50 0 0 500 1000 1500 2000 time: Day 2500 3000 3500 4000 Fig. 23. Relation between P sorption and time in soil column from 0 to 1 m. 32 Lin Yu TRITA LWR Degree Project 12:01 Based on equation (33), the time is varied from 1 to 4000 days to get the relation between sorption quantity and time for a 1-m soil column, which can be seen in Fig. 22. The sorption P in the soil column seems to have a linear relation with time before the concentration start to increase at depth 1 m, when the concentration at 1 m starts to increase; the sorption curve slows to increase and finally stops at a peak value when the concentration reaches the inflow concentration. The reasons for this are the assumption of instant sorption and the homogeneity and isotrope of the soil. Once the sewage enters a modeled layer, instant sorption would happen, and before this layer reaches inflow concentration, the next modeled layer will not have sorption. Since the inflow concentration and flow velocity are set to be the same in all the three sites, it is not strange to have the sorption curves in Fig. 23 paralleled, because the rates of the curves are the inflow P into the soil column per unit time. The disficiency of the sorption velocity prediction in this study is quite obvious. Since only the fast sorption is considered in this study, the sorption velocity attained by this model turns out to be very linear and starts with an abrupt big velue. The need for the sorption isotherm is quite essential in the analysis of sorption rate, at the same time, as discussed in previous section, batch experiment could also be a big uncertainty in the sorption rate predisction, because it would more or less accelerate the sorption process. If the intermittent flow is also considered in the model, the situation of sorption rate could be even more complex since desorption process might also happen in the system. Anyhow, it is possible to analyse the sorption capacity and sorption rate of the system if the concentration curve is well studied. 3.4. D ISCUSSION ON MODELING RESULTS 3.4.1. Factors influencing the longevity of soil column From the results of modeling study, the most sensitive factors for P concentration in soil column to reach critical concentration are the flow velocity and the P sorption capacity of the soil. Lower flow velocity and higher P sorption capacity extend the longevity of an infiltration bed. A literature study on different soil shows that soil with higher proportion of small-size particles such as clay tends to have higher phosphorus sorption capacity (McGechen et al., 2002a; b). Normally clay soil has lower bulk density and higher volumetric water content than the soil in this study, which is coarse sand. The model results also show that a lower bulk density and a higher volumetric water content will extend the longevity of the soil column. So a conclusion can be drawn that soil with a high proportion of small-sized particles also has longer longevity when used as soil column for infiltration. It is easier to understand that a higher P sorption capacity would lead to higher longevity of soil column. A much longer longevity is estimated in Luvehult than in the other two sites. It is obvious to notice that in a sample with soil from surface horizons Luvehult, higher solution P concentrations are measured after batch experiments, and much higher Sini are estimated also. It is also concluded in this study that oxalate-extractable Al and Fe are correlated to P sorption, of which Al is more related to the fast reaction and Fe is more related to the slow reaction. Meanwhile, other researchers have pointed out that soils containing high proportions of Al or Fe oxide minerals have particularly high P sorption capacity (Bowden et al., 1977; Robertson, 2003; Zanini et al., 2003). In a comparative study, Singh et al. (2005) also found highest P sorption with high amounts of Fe, Al and clay particles. 33 Modeling the Longevity of Infiltration System for Phosphorus Removal Another very sensitive parameter in the model is the average pore velocity, in this thesis mostly referred to as the flow velocity. A constant insistent influent is assumed in the conceptual model, with a quite high flow velocity 0.03 m/D. From the sensitivity analysis, it can be noticed that in lower range of flow velocity, the longevity of a soil column is very sensitive to the change of flow velocity. As a matter of fact, the assumption made in conceptual models about the flow velocity can be quite unrealistic in experimental column studies, not to mention in the real infiltration system. However, principally lower velocity or in other lower sewage load would result in a longer longevity of soil column. 3.4.2. Longevity of infiltration bed and evaluations with current method The results from the Basic Scenario show the longevity estimation based on the current model. Compared to the service time of those infiltration sites, the longevity estimation by this model is relatively short. From the Fig. 8(b), it is clearly noticed that the estimated Sini is much smaller than the measured Pox, which indicates the necessity to add time as a controlling factor for P sorption in soil. However, it is really difficult to make a simple judgment as to whether the estimated longevity after applying sorption kinetics would be bigger or smaller than the previous model, since the ADE equation in the model would change. In order to make a comparison with the first method mentioned in the introduction part, the inflow P concentration was recalibrated according to the literature (Xu and et al., 2006; Seo et al., 2005; Drizo et al., 2002; Drizo et al., 1999). This gives a new inflow P concentration of 9.333 mg/L. Based on this inflow, the estimated longevity is shown in Fig. 22. The calculated maximum sorption P under 9.333 mg/L P inflow for Kn, Lu and Ri are 0.247, 0.255 and 0.363 g/kg separately. According to Fig. 24, this will lead to longevities of 1243, 1746 and 1295 days for sites Kn, Lu and Ri. Considering the difference of the substrates’ bulk densities, the estimated longevity is of the same order as those in the literature study. From the results in section 3.3.7, it can be seen that for the 1-m soil column, all the P from inflow would be sorbed instantly before the concentration at 1 m starts to increase. Since in this model, instant equilibrium is assumed in every layer. So when the concentration at 1 m depth starts to increase, in fact the previous soil layer has already reached its sorption maximum according to equation (17). X: 1865 Y: 9.333 10 9 X: 2128 Y: 9.333 8 Kn Ri 7 concentration: mg/L X: 2507 Y: 9.333 6 Lu 5 4 3 2 X: 1243 X: 1746 Y: 1.004 Y: 1.003 1 0 X: 1295 Y: 1.001 0 500 1000 1500 2000 2500 3000 time: Day 3500 4000 4500 5000 Fig. 24. Estimated longevity of soil columns under sewage P concentration of 9.333 mg/L. 34 Lin Yu TRITA LWR Degree Project 12:01 Therefore, although the theoretical definition of longevity in the first method from literature review is wrong, it gives a result of system longevity that is very close compared to the result from the model study. However, another big problem is the phosphorus sorption capacity (Spsc) used in this method. According to Drizo et al. (2002), they increase the P concentration in inflow until the substrate no longer sorbs more phosphate, and the maximum sorption is then taken as Spsc. Firstly, this sorption capacity is only the maximum fast P pool of the substrate since the incubation time of their study is very short. Secondly, for normal sewage in infiltration systems, it is unknown if this Spsc would be reached by the soil under low inflow concentration, and if this can be reached, it must take a really long period of sorption, which can be concluded from Fig. 8(b). For the second method from literature study, since no P sorption quantity is measured in their study, it is really difficult to compare with the model estimation. However, during the estimated longevity in the second method, the substrate is quite reliable for P removal since it is based on experiment data. The problems in those studies are that the estimated longevity might be underestimated, which may lead to substrates being changed too early compared to their real longevity. 4. F URTHER STUDY 4.1. Boundary Condition One uncertainty of this model is the assumption for the boundary condition at C(2,t). The correct boundary condition should be that the concentration at infinite distance is always 0, but that is really unrealistic for the numerical solution of the PDE equation. Normally the boundary of the model should be set as the boundary of the study area, but due to the lack of relative data, the model boundary is enlarged in order to ease up the influence of the unsure boundary condition on the study area. This is also the reason why the modeling time is set to be quite long, so that all the modeling results of the study area are ideal results from advection, dispersion and retardation. Further research needs to be done to make a better boundary condition for the model, or as Van der Zee et al. (1992) did, discuss about alternative boundary conditions. 4.2. Flow velocity & hydrogeology The estimation of flow velocity in the study is really simplified and not much hydrogeological details are considered in the model of soil column. In reality, groundwater flow is quite complicated and influenced by many factors. A possible way of acquiring flow velocity is solving flow equation, which in the unsaturated condition is known as Richards’ equation. This also requires many hydrogeology properties as input, and boundary conditions as well, because Richards’ equation itself is also a partial differential equation. Nicholas J. Jarvis and colleagues have done modeling work with a model named MACRO, which also includes macropore flow. Further development of the model could also try to coup the flow equation with the ADE equation in order to have more accurate flow velocity input for the model. This effort can also help the model to be applicable not only in soil column study in the lab, but also in some real infiltration systems with well studied soil properties. 4.3. Desorption & Operation Mode Some of the infiltration beds are divided into two or more parts. One of them is run for sewage treatment, while the rest of them are kept free in order to recover the treatment capacity of the soil. So it is an interesting 35 Modeling the Longevity of Infiltration System for Phosphorus Removal topic to study the recovered capacity of soil column for P removal. However, the recovery of P sorption capacity of soil is mainly controlled by desorption process, which are not discussed in detail in this study. Because the recovery process is more controlled by natural precipitation rather than the sewage inflow, climate data are also necessary for the recovery capacity modeling. Besides, for most of infiltration beds, the sewage inflows are not always consistent, and intermittent sewage inflow also might include the process of desorption. Further study can focus on the desorption isotherms of phosphorus in the soil, the combine of both sorption and desorption in the transport model would give more reasonable consequence for the longevity study of infiltration beds. It is suggested to use sorption/desorption kinetics in further development of the model, so that the model would be more applicable to the real infiltration system. 4.4. Influence of pH Further study can also focus on ascertaining the pH influence on the P sorption capacity, by designing of new experiment strategies. By integrating the isotherms which include the pH into the ADE equation, new improved models can be derived for simulation of the longevity of infiltration beds. 36 Lin Yu TRITA LWR Degree Project 12:01 R EFERENCES Appelo, C.A.J., Postma, D. 2005. Geochemistry, Groundwater and Pollution. A. A. Balkema Publishers: New York; pp. 253 – 279. Barrow, N.J. 1978. The description of phosphate adsorption curves. Soil Science. 29: 447–462. Bowden, J.W., Posner, A., Quirk, J. 1977. Ionic adsorption on variable charge mineral surfaces. Theoretical-charge development and titration curves. Australian Journal of Soil Research. 15: 121–136. Cheung, K.C., Venkitachalam, T.H. 2006. Kinetic studies on phosphorus sorption by selected soil amendments for septic tank effluent renovation. Environmental Geochemistry and Health. 28:121–131. Cucarella, V., Renman, G. 2009. Phosphorus Sorption Capacity of Filter Materials Used for On-site Wastewater Treatment Determined in Batch Experiments–A Comparative Study. Journal of Environmental Quality. 38(2), 381-392. Delleur, J. 1999. The handbook of groundwater engineering. CRC Press LLC: Boca Raton; pp. 96-102. Drizo, A., Comeau, Y., Forget, C., Chapuis, R.P. 2002. Phosphorus Saturation Potential: A Parameter for Estimating the Longevity of Constructed Wetland Systems. Environmental Science and Technology. 36 (21), 4642-4648. Drizo, A., Frost, C.A., Grace, J., Smith, K.A. 1999. Physical-chemical screening of phosphate-removing substrates for use in constructed wetland systems. Water Research 33(17): 3595 - 3602. Eveborn, D., Gustafsson, J.P., Holm, C. 2009. Fosfor i infiltrationsbäddar – fastläggning, rörlighet och bedömningsmetoder. Svenskt Vatten Utveckling, Rapport nr 2009-07, Stockholm. Gustafsson, J.P., Jacks, G., , Simonsson, M., Nilsson, I. 2007. Soil and water chemistry. KTH Department of Land and Water Resources Engineering, Stockholm; pp. 60 – 72. Heistad, A., Paruch, A.M., Vråle, L., Adam, K., Jenssen, P.D. 2006. A high–performance compact filter system treating domestic wastewater. Ecological Engineering. 28: 374–379. Hocking, M.B. 2006. Handbook of Chemical Technology and Pollution Control (third edition). Elsevier Science & Technology Books, Amsterdam; p. 297. Hooda, P.S., Rendell, A.R., Edwards, A.C., Withers, P.J.A., Aitken, M.N., Truesdale, V.W. 2000. Relating soil phosphorus indices to potential phosphorus release to water. Journal of Environmental Quality. 29: 1166– 1171. Jalali, M., Khanlar, Z.V. 2011. The Impacts of Common Ions and Electrolyte Concentration on the Release of P from Some Calcareous Soils. Arid Land Research and Management. 25: 217 – 233. Jalali, M., Zinli, N.A.M. 2011. Kinetics of phosphorus release from calcareous soils under different land use in Iran. J. Plant Nutr. Soil Sci. 174: 38 – 46. Johansson, M. 2008. The market for onsite sustainable sanitation technologies – an example from Sweden. In Report of the World Water Week Seminar: Europe’s Sanitation Problem: Stockholm. Kafkafi, U., Posner, A.M., Quirk, J.P. 1967. Desorption of phosphate from kaolinite. Soil Science Society of America Proceedings. 31: 348–353. 37 Modeling the Longevity of Infiltration System for Phosphorus Removal Kong, D. 2009. Phosphate sorption in soil infiltration systems for wastewater treatment. TRITA LWR Degree Project 09:19. KTH, Department of Land and Water Resources Engineering, Stockholm. Laak, R. 1986. Wastewater engineering design for unsewered areas. Technomic Publishers, The Hague, Netherlands. Lookman, R., Freese, D., Merckx, R., Vlassek, K., van Riemsdijk, W.H. 1995. Long term kinetics of phosphate release from soil. Environmental Science and Technology. 29: 1569–1575. Mathews, J.H., Fink, K.D. 2004. Numerical Methods Using Matlab (4th Edition). Prentice Hall, Upper Saddle River; pp. 514 – 554. McGechan, M.B., Lewis, D.R. 2002. Sorption of Phosphorus by Soil, Part 1: Principles, Equations and Models. Biosystems Engineering. 82 (1): 1–24. McGechan, M.B. 2002. Sorption of Phosphorus by Soil, Part 2: Measurement Methods, Results and Model Parameter Values. Biosystems Engineering. 82 (2): 115–130. McWorter, S. 1977. Ground-water hydrology and hydraulics. Water Resources Publications, Highlands Ranch; pp. 258 -259. Notodarmojo, S., Ho, G.E., Scott, W.D., Davis, G.B. 1991. Modeling phosphorus transport in soils and groundwater with two-consecutive reactions. Water Research. 25(10): 1205-1216. Parkhurst, D.L., Appelo, C.A.J. 1999. User’s guide to PHREEQC (Version 2) – a computer program for speciation, batch reaction, onedimensional transport, and inverse geochemical calculations U.S. Geological Survey Water-Resources Investigations Report 99-4259: pp. 44 – 52. Renman, A., Renman, G. 2010. Long-term phosphate removal by the calcium-silicate material Polonite in wastewater filtration systems. Chemosphere. 79: 659–664. Robertson, W.D. 2003. Enhanced Attenuation of Septic System Phosphate in Nocalcareous Sediments. Ground Water. 41: 48 – 56. Sakadevan, K., Bavor H.J. 1998. Phosphate adsorption characteristics of soils, slags and zeolite to be used as substrate in constructed wetland systems. Water Research. 32: 393–399. Scheidegger, A. 1960. Physics of Flow Through Porous Media. University of Toronto Press, Toronto, Canada. Schnoor, J.L. 1996. Environmental modeling: fate and transport of pollutants in water, air and soil. Wiley, New York; pp. 146 – 180. Seo, D.C., Cho, J.S., Lee, H.J., Heo, J.S. 2005. Phosphorus retention capacity of filter media for estimating the longevity of constructed wetland. Water Research. 39: 2445–2457. Singh, B.R., Krogstad, T., Shivay, Y.S., Shivakumar, B.G., Bakkegard, M. 2005. Phosphorus fractionation and sorption in P-enriched soils of Norway. Nutrient Cycling in Agroecosystems. 73: 245 – 256. Spiteri , C., Slomp, C.P., Regnier, P., Meile, C., van Cappellen, P.. 2007. Modeling the geochemical fate and transport of wastewater-derived phosphorus in contrasting groundwater systems. Journal of Contaminant Hydrology. 92: 87–108. van der Zee, S.E.A.T.M., Gjaltema, A. 1992. Simulation of phosphate transport in soil columns: I. Model development. Geoderma. 52 (1-2): 87–109. 38 Lin Yu TRITA LWR Degree Project 12:01 van der Zee, S.E.A.T.M., Gjaltema A, van Riemsdijk, W.H., de Haan, F.A.M. 1992. Simulation of phosphate transport in soil columns. II. Simulation results. Geoderma. 52 (1-2): 111–132. Wang, Q., Li, Y. 2010. Phosphorus adsorption and desorption behavior on sediments of different origins. Journal of Soils and Sediments. 10: 1159 – 1173. Wang, S., Jin, S., Panga, Y., Zhao, H., Zhou, X. 2005. The study of the effect of pH on phosphate sorption by different trophic lake sediments. Journal of Colloid and Interface Science. 285: 448 – 457. Weiss, P., Eveborn, D., Kärrman, E., Gustafsson, J. P.. 2008. Environmental systems analysis of four on-site wastewater treatment options. Conservation and Recycling. 52(10): 1153–1161. Xu, D., Xu, J., Wu, J., Muhammad, A. 2006. Studies on the phosphorus sorption capacity of substrates used in constructed wetland systems. Chemosphere. 63: 344–352. Zanini, L., Robertson, W.D., Ptacek, C.J., Schiff, S.L., Mayer, T. 1998. Phosphorus characterization in sediments impacted by septic effluent at four sites in central Canada. Journal of Contaminant Hydrology. 33: 405 – 429. O THER REFERENCES Cornforth, I.S. 2009. The fate of phosphate fertilizers in soil. New Zealand Institute of Chemistry. Web: http://nzic.org.nz/ChemProcesses/soils/2D.pdf. Last accessed 2011-10-29. Minnesota University Online literature. Web: http://www.extension.umn.edu/distribution/cropsystems/DC6795. html. Last accessed 2011-08-23. Wikipedia. Web: http://en.wikipedia.org/wiki/MATLAB. Last accessed 2011-08-21. 39 Modeling the Longevity of Infiltration System for Phosphorus Removal 40 Lin Yu TRITA LWR Degree Project 12:01 A PENDIX I – M EASURED DRY WEIGHT OF SOIL SAMPLES Measured dry weight of soil samples Sample Dry Weight (g/g) Ri ref 1 0.978 Kn ref 1 0.965 Lu ref grov 0.972 Tu ref 0.963 Gl 0-5 0.836 Ri 0-5 0.902 Tu 5-15 0.878 Ha 5-15 0.923 Kn 5-15 0.926 Ri 5-15 0.946 Lu 5-15 0.925 Ha 0-5 0.942 Lu 0-5 0.907 Kn 0-5 0.920 Gl ref 0-5 0.825 Gl ref 5-15 0.879 Ha ref 2 0.976 Gl 5-15 0.822 Tu 0-5 0.332 Ha ref 1 0.970 1 Modeling the Longevity of Infiltration System for Phosphorus Removal A PENDIX II – M EASURED OXALATE - SOLUBLE PHOSPHORUS OF SOIL SAMPLES Oxalate-soluble Phosphorus Sample Oxalate-soluble P mg/g Gl ref 0-5 0.202 Gl ref 5-15 0.109 Gl 0-5 0.274 Gl 5-15 0.215 Ha 0-5 0.248 Ha 5-15 0.200 Ha ref 1 0.0134 Ha ref 2 0.0115 Kn 0-5 0.168 Kn 5-15 0.164 Kn ref 0.0480 Lu 0-5 1.143 Lu 5-15 1.043 Lu ref grov 0.0695 Ri 0-5 0.221 Ri 5-15 0.216 Ri ref 1 0.0554 Tu 0-5 2.226 Tu 5-15 0.323 Tu ref 0.152 2 Lin Yu TRITA LWR Degree Project 12:01 A PPENDIX III: B ATCH E XPERIMENT LAB DESIGN 27: 10 ml A, 0.5 ml P, 19.5 ml H2O 28: 10 ml A, 1 ml P, 19 ml H2O 29: 10 ml A, 1.5 ml P, 18.5 ml H2O 30: 10 ml A, 2 ml P, 18 ml H2O 31: 10 ml A. 3 ml P, 17 ml H2O 32: 10 ml A, 5 ml P, 15 ml H2O Series A - 5d equilibration of soils. Solutions: A = 0.03 M NaNO3 B = 0.03 M HNO3 E = 0.03 M NaOH P = 3 mM NaH2PO4 PL = 0.3 mM NaH2PO4 4 g of Lu 0-5 33: 10 ml A, 20 ml H2O 34: 10 ml A, 2 ml PL, 18 ml H2O 35: 10 ml A, 0.5 ml P, 19.5 ml H2O 36: 10 ml A, 1 ml P, 19 ml H2O 37: 10 ml A, 1.5 ml P, 18.5 ml H2O 38: 10 ml A, 2 ml P, 18 ml H2O 39: 10 ml A. 3 ml P, 17 ml H2O 40: 10 ml A, 5 ml P, 15 ml H2O 4 g of Kn ref 1 1: 10 ml A, 20 ml H2O 2: 10 ml A, 2 ml PL, 18 ml H2O 3: 10 ml A, 0.5 ml P, 19.5 ml H2O 4: 10 ml A, 1 ml P, 19 ml H2O 5: 10 ml A, 1.5 ml P, 18.5 ml H2O 6: 10 ml A, 2 ml P, 18 ml H2O 7: 10 ml A. 3 ml P, 17 ml H2O 8: 10 ml A, 5 ml P, 15 ml H2O 4 g of Lu 5-15 41: 10 ml A, 20 ml H2O 42: 10 ml A, 2 ml PL, 18 ml H2O 43: 10 ml A, 0.5 ml P, 19.5 ml H2O 44: 10 ml A, 1 ml P, 19 ml H2O 45: 10 ml A, 1.5 ml P, 18.5 ml H2O 46: 10 ml A, 2 ml P, 18 ml H2O 47: 10 ml A. 3 ml P, 17 ml H2O 48: 10 ml A, 5 ml P, 15 ml H2O 4 g of Kn 0-5 9: 10 ml A, 20 ml H2O 10: 10 ml A, 2 ml PL, 18 ml H2O 11: 10 ml A, 0.5 ml P, 19.5 ml H2O 12: 10 ml A, 1 ml P, 19 ml H2O 13: 10 ml A, 1.5 ml P, 18.5 ml H2O 14: 10 ml A, 2 ml P, 18 ml H2O 15: 10 ml A. 3 ml P, 17 ml H2O 16: 10 ml A, 5 ml P, 15 ml H2O 4 g of Kn 5-15 17: 10 ml A, 20 ml H2O 18: 10 ml A, 2 ml PL, 18 ml H2O 19: 10 ml A, 0.5 ml P, 19.5 ml H2O 20: 10 ml A, 1 ml P, 19 ml H2O 21: 10 ml A, 1.5 ml P, 18.5 ml H2O 22: 10 ml A, 2 ml P, 18 ml H2O 23: 10 ml A. 3 ml P, 17 ml H2O 24: 10 ml A, 5 ml P, 15 ml H2O 4 g of Lu ref grov 25: 10 ml A, 20 ml H2O 26: 10 ml A, 2 ml PL, 18 ml H2O 3 Modeling the Longevity of Infiltration System for Phosphorus Removal 28: 10 ml A, 1 ml P, 19 ml H2O 29: 10 ml A, 1.5 ml P, 18.5 ml H2O 30: 10 ml A, 2 ml P, 18 ml H2O 31: 10 ml A. 3 ml P, 17 ml H2O 32: 10 ml A, 5 ml P, 15 ml H2O Series B - 5d equilibration of soils. Solutions: A = 0.03 M NaNO3 B = 0.03 M HNO3 E = 0.03 M NaOH P = 3 mM NaH2PO4 PL = 0.3 mM NaH2PO4 4 g of Tu 0-5 33: 10 ml A, 20 ml H2O 34: 10 ml A, 2 ml PL, 18 ml H2O 35: 10 ml A, 0.5 ml P, 19.5 ml H2O 36: 10 ml A, 1 ml P, 19 ml H2O 37: 10 ml A, 1.5 ml P, 18.5 ml H2O 38: 10 ml A, 2 ml P, 18 ml H2O 39: 10 ml A. 3 ml P, 17 ml H2O 40: 10 ml A, 5 ml P, 15 ml H2O 4 g of Ri ref 1 1: 10 ml A, 20 ml H2O 2: 10 ml A, 2 ml PL, 18 ml H2O 3: 10 ml A, 0.5 ml P, 19.5 ml H2O 4: 10 ml A, 1 ml P, 19 ml H2O 5: 10 ml A, 1.5 ml P, 18.5 ml H2O 6: 10 ml A, 2 ml P, 18 ml H2O 7: 10 ml A. 3 ml P, 17 ml H2O 8: 10 ml A, 5 ml P, 15 ml H2O 4 g of Tu 5-15 41: 10 ml A, 20 ml H2O 42: 10 ml A, 2 ml PL, 18 ml H2O 43: 10 ml A, 0.5 ml P, 19.5 ml H2O 44: 10 ml A, 1 ml P, 19 ml H2O 45: 10 ml A, 1.5 ml P, 18.5 ml H2O 46: 10 ml A, 2 ml P, 18 ml H2O 47: 10 ml A. 3 ml P, 17 ml H2O 48: 10 ml A, 5 ml P, 15 ml H2O 4 g of Ri 0-5 9: 10 ml A, 20 ml H2O 10: 10 ml A, 2 ml PL, 18 ml H2O 11: 10 ml A, 0.5 ml P, 19.5 ml H2O 12: 10 ml A, 1 ml P, 19 ml H2O 13: 10 ml A, 1.5 ml P, 18.5 ml H2O 14: 10 ml A, 2 ml P, 18 ml H2O 15: 10 ml A. 3 ml P, 17 ml H2O 16: 10 ml A, 5 ml P, 15 ml H2O 4 g of Ri 5-15 17: 10 ml A, 20 ml H2O 18: 10 ml A, 2 ml PL, 18 ml H2O 19: 10 ml A, 0.5 ml P, 19.5 ml H2O 20: 10 ml A, 1 ml P, 19 ml H2O 21: 10 ml A, 1.5 ml P, 18.5 ml H2O 22: 10 ml A, 2 ml P, 18 ml H2O 23: 10 ml A. 3 ml P, 17 ml H2O 24: 10 ml A, 5 ml P, 15 ml H2O 4 g of Tu ref 25: 10 ml A, 20 ml H2O 26: 10 ml A, 2 ml PL, 18 ml H2O 27: 10 ml A, 0.5 ml P, 19.5 ml H2O 4 Lin Yu TRITA LWR Degree Project 12:01 26: 27: 28: 29: 30: Series C - 5d equilibration of soils. Solutions: A = 0.03 M NaNO3 B = 0.03 M HNO3 E = 0.03 M NaOH 4 g of Ri 5-15 31: 32: 33: 34: 35: 36: 4 g of Kn 0-5 1: 2: 3: 4: 5: 6: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 37: 38: 39: 40: 41: 42: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 43: 44: 45: 46: 47: 48: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 4 g of Lu 5-15 19: 20: 21: 22: 23: 24: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 4 g of Ri 0-5 25: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 4 g of Tu 5-15 4 g of Lu 0-5 13: 14: 15: 16: 17: 18: 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 4 g of Tu 0-5 4 g of Kn 5-15 7: 8: 9: 10: 11: 12: 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O 10 ml A, 3 ml B, 17 ml H2O 5 10 ml A, 3 ml B, 17 ml H2O 10 ml A, 2 ml B, 18 ml H2O 10 ml A, 1 ml B, 19 ml H2O 10 ml A, 0.5 ml B, 19.5 ml H2O 10 ml A, 20 ml H2O 10 ml A, 0.5 ml E, 19.5 ml H2O Modeling the Longevity of Infiltration System for Phosphorus Removal A PPENDIX IV: E MPIRICAL DATA FOR POROSITY CALCULATION Empirical data for porosity calculation Material Total Porosity, n Range Arithmetic Mean Sandstone (medium) 0.14 - 0.49 0.34 Siltstone 0.21 – 0.41 0.35 Sand (fine) 0.25 – 0.53 0.43 Sand (coarse) 0.31 – 0.46 0.39 Gravel (fine) 0.25 – 0.38 0.34 Gravel (coarse) 0.24 – 0.36 0.28 Silt 0.34 – 0.51 0.45 Clay 0.34 – 0.57 0.42 Limestone 0.07 -0.52 0.3 Weathered granite 0.34 -0.57 0.45 Weathered gabbro 0.42 – 0.45 0.43 Basalt 0.03 - 0.35 0.17 Schist 0.04 – 0.49 0.38 Source: McWorter and Sunada (1977). h 6 Lin Yu TRITA LWR Degree Project 12:01 A PPENDIX V: C OMPARISON OF DESORBED P BETWEEN ACID SAMPLE AND NON - ACID SAMPLE OF P H DEPENDENCE TEST (X AXIS : SAMPLE NUMBER ; Y AXIS : P CONCENTRATION MG /L) 2500 2000 2000 1500 Kn 0‐5 1500 Kn 5‐15 1000 1000 Kn 0‐5 acid 500 Kn 5‐15 acid 500 0 0 1 2 3 4 5 6 1 3000 2500 2500 2000 2000 Lu 0‐5 4 5 6 Lu 5‐15 acid 500 0 Lu 5‐15 1000 Lu 0‐5 acid 500 3 1500 1500 1000 2 0 1 2 3 4 5 6 1 2 3 4 5 6 5000 7000 6000 5000 4000 3000 2000 1000 0 4000 Ri 5‐15 3000 Ri 0‐5 2000 Ri 0‐5 acid Ri 5‐15 acid 1000 0 1 2 3 4 5 6 1 7 2 3 4 5 6 Modeling the Longevity of Infiltration System for Phosphorus Removal A PPENDIX VI: M ATLAB C ODES FOR M ODELING pdeadeT.m: main m-file for the solution of the ADE equation in the model function pdeadeT % input parameters m = 0; a=2; b=1000; x = linspace(0,a,a*100); t = linspace(0,b,b*10);% n is the estimated time for x=1 to reach 0.1mg/L sol = pdepe(m,@pdeadeTpde,@pdeadeTic,@pdeadeTbc,x,t); u = sol(:,:,1); Fig. plot(t,u(:,100),'r'); % define the ADE equation function [c,f,s] = pdeadeTpde(x,t,u,DuDx) a=2; U=0.03; alpha=0.1*a; [Kf,I]=isotherms(sorptions); [theta,porosity,BD]=soilp(soilprofile,Dryweight); DL=U*alpha; v=U/mean(theta(3,:)); c=1+mean(BD(3,:))/mean(theta(3,:))*I(3)*Kf(3)*u^(I(3)-1); f=DL*DuDx; s=-v*DuDx; % define initial condition function u0=pdeadeTic(x) c1=0.015; u0=c1; % define boundary condition function [pl,ql,pr,qr] = pdeadeTbc(xl,ul,xr,ur,t) b=1000; c1=0.015; c2=5; pl=ul-c2; ql=0; pr=ur(1)-c1-(1-c1)/b*t; qr=0; 8 Lin Yu TRITA LWR Degree Project 12:01 Isotherm.m: the m-file for isorthem plotting which returns parameter Kf and I to the main program function [Kf,I]=isotherms(sorptions) load sorptions.txt; j=length(sorptions); K=zeros(j,1); K1=zeros(j,1); K=sorptions(:,3); for num=1:j K1(num,1)=log10((sorptions(num,1)+sorptions(num,2))/1000/0.004/so rptions(num,4)); end Kn=[K(1:21) K1(1:21)];Kn0=[K(1:7) K1(1:7)];Kn5=[K(8:14) K1(8:14)];Kn15=[K(15:21) K1(15:21)]; Lu=[K(22:41) K1(22:41)];Lu0=[K(22:27) K1(22:27)];Lu5=[K(28:34) K1(28:34)];Lu15=[K(35:41) K1(35:41)]; Ri=[K(42:62) K1(42:62)];Ri0=[K(42:48) K1(42:48)];Ri5=[K(49:55) K1(49:55)];Ri15=[K(56:62) K1(56:62)]; m1=sorptions(:,1);m2=sorptions(:,2);m3=sorptions(:,4); % select the best value for sampling site Kn [ c1,c2 ] = MultiLineReg( Kn0(:,1),Kn0(:,2) ); [ c3,c4 ] = MultiLineReg( Kn5(:,1),Kn5(:,2) ); [ c5,c6 ] = MultiLineReg( Kn15(:,1),Kn15(:,2) ); [ c7,c8 ] = MultiLineReg( Kn(:,1),Kn(:,2) ); mx=c2+c4+c6+c8*3; R1=linspace(0.8*m1(1),1.2*m1(1),50);R2=linspace(0.8*m1(8),1.2*m1(8), 50);R3=linspace(0.8*m1(15),1.2*m1(15),50); mx=0;KnB=m1(1:21); for i=1:50 for j=1:50 for k=1:50 m4(1:7)=R1(i); m4(8:14)=R2(j); m4(15:21)=R3(k); for l=1:21 K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l)); end Kn=[K(1:21) K1(1:21)];Kn0=[K(1:7) K1(1:7)];Kn5=[K(8:14) K1(8:14)];Kn15=[K(15:21) K1(15:21)]; [ c1,c2 ] = MultiLineReg( Kn0(:,1),Kn0(:,2) ); [ c3,c4 ] = MultiLineReg( Kn5(:,1),Kn5(:,2) ); [ c5,c6 ] = MultiLineReg( Kn15(:,1),Kn15(:,2) ); [ c7,c8 ] = MultiLineReg( Kn(:,1),Kn(:,2) ); K2=c2+c4+c6+c8*3; if K2>mx mx=K2; KnB=m4(1:21); 9 Modeling the Longevity of Infiltration System for Phosphorus Removal BKfKn=c7; end end end end Kf(1)=BKfKn(1); I(1)=BKfKn(2); % select the best value for sampling site Lu [ c1,c2 ] = MultiLineReg( Lu0(:,1),Lu0(:,2) ); [ c3,c4 ] = MultiLineReg( Lu5(:,1),Lu5(:,2) ); [ c5,c6 ] = MultiLineReg( Lu15(:,1),Lu15(:,2) ); [ c7,c8 ] = MultiLineReg( Lu(:,1),Lu(:,2) ); mx=c2+c4+c6+c8*3; R4=linspace(0.8*m1(22),1.2*m1(22),50);R5=linspace(0.8*m1(28),1.2*m1 (28),50);R6=linspace(0.8*m1(35),1.2*m1(35),50); mx=0;LuB=m1(22:41); for i=1:50 for j=1:50 for k=1:50 m4(22:27)=R4(i); m4(28:34)=R5(j); m4(35:42)=R6(k); for l=22:42 K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l)); end Lu=[K(22:41) K1(22:41)];Lu0=[K(22:27) K1(22:27)];Lu5=[K(28:34) K1(28:34)];Lu15=[K(35:41) K1(35:41)]; [ c1,c2 ] = MultiLineReg( Lu0(:,1),Lu0(:,2) ); [ c3,c4 ] = MultiLineReg( Lu5(:,1),Lu5(:,2) ); [ c5,c6 ] = MultiLineReg( Lu15(:,1),Lu15(:,2) ); [ c7,c8 ] = MultiLineReg( Lu(:,1),Lu(:,2) ); K2=c2+c4+c6+c8*3; if K2>mx mx=K2; LuB=m4(22:41); BKfLu=c7; end end end end Kf(2)=BKfLu(1); I(2)=BKfLu(2); %Calculation of the best value for sampling site Ri [ c1,c2 ] = MultiLineReg( Ri0(:,1),Ri0(:,2) ); 10 Lin Yu TRITA LWR Degree Project 12:01 [ c3,c4 ] = MultiLineReg( Ri5(:,1),Ri5(:,2) ); [ c5,c6 ] = MultiLineReg( Ri15(:,1),Ri15(:,2) ); [ c7,c8 ] = MultiLineReg( Ri(:,1),Ri(:,2) ); mx=c2+c4+c6+c8*3; R7=linspace(0.8*m1(42),1.2*m1(42),50);R8=linspace(0.8*m1(49),1.2*m1 (49),50);R9=linspace(0.8*m1(56),1.2*m1(56),50); mx=0;RiB=m1(42:62); for i=1:50 for j=1:50 for k=1:50 m4(42:48)=R7(i); m4(49:55)=R8(j); m4(56:62)=R9(k); for l=42:62 K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l)); end Ri=[K(42:62) K1(42:62)];Ri0=[K(42:48) K1(42:48)];Ri5=[K(49:55) K1(49:55)];Ri15=[K(56:62) K1(56:62)]; [ c1,c2 ] = MultiLineReg( Ri0(:,1),Ri0(:,2) ); [ c3,c4 ] = MultiLineReg( Ri5(:,1),Ri5(:,2) ); [ c5,c6 ] = MultiLineReg( Ri15(:,1),Ri15(:,2) ); [ c7,c8 ] = MultiLineReg( Ri(:,1),Ri(:,2) ); K2=c2+c4+c6+c8*3; if K2>mx mx=K2; RiB=m4(42:62); BKfRi=c7; end end end end Kf(3)=BKfRi(1); I(3)=BKfRi(2); AllB=[KnB LuB RiB]; % the final initial sorption data %calculation of Freundlich coefficients from related data, all the input are from %batch experiments 11 Modeling the Longevity of Infiltration System for Phosphorus Removal Soilp.m: the m-file for calculation of soil property parameters for the main m-file function [theta,porosity,BD]=soilp(soilprofile,Dryweight) load soilprofile.txt; load Dryweight.txt; ProR=soilprofile(9,:)'; ProM=soilprofile(1:8,:)*ProR; porosity=[ProM(6) ProM(8) ProM(5) ProM(6) ProM(8) ProM(5)]'; DryInput=[Dryweight(14) Dryweight(9) Dryweight(13) Dryweight(11) Dryweight(6) Dryweight(10)]; for i=1:3 Volume(i,:)=(DryInput(i,:)/2.4)*100/(100-porosity(i)); end BD=1./Volume; WaterInput=ones(3,2)-DryInput; theta=WaterInput./Volume; 12 Lin Yu TRITA LWR Degree Project 12:01 MultiLineReg.m: the m-file for the multi-linear regression of the data, which returns r2 to the Isotherm.m function [ RegCoef,R2,F,FX,TX ] = MultiLineReg( X,Y ) format long; sz=size(X); N=sz(1); nn=sz(2); RegCoef=zeros(nn+1,1); Z=mean(X); yp=mean(Y); A=transpose(X)*X-N*transpose(Z)*Z; C=transpose(X)*Y-N*transpose(Z)*yp; RegCoef(2:nn+1)=A\C; RegCoef(1)=yp-Z*RegCoef(2:nn+1); S=norm(Y)^2-N*yp^2; YR=X*RegCoef(2:nn+1)+RegCoef(1)*ones(N,1); U=transpose(RegCoef(2:nn+1))*C; Q=S-U; R=sqrt(U/S); R2=U/S; UR=U/(length(RegCoef)-1); QR=Q/(N-length(RegCoef)); s=sqrt(QR); inA=inv(A); F=UR/QR; for i=1:length(RegCoef)-1 FX(i)=RegCoef(i+1)^2/inA(i,i)/QR; TX(i)=RegCoef(i+1)/sqrt(inA(i,i)*s); end format short; 13

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