Water Air Soil Pollut (2014) 225:1794 DOI 10.1007/s11270-013-1794-8
A Simplified Transfer Function for Estimating Saturated Hydraulic Conductivity of Porous Drainage Filters Eriona Canga & Bo Vangsø Iversen & Charlotte Kjaergaard
Received: 17 July 2013 / Accepted: 22 October 2013 / Published online: 29 November 2013 # Springer Science+Business Media Dordrecht 2013
Abstract Knowledge of the saturated hydraulic conductivity (Ksat) of porous filters used in water treatment technologies is important for optimizing the retention of nutrients and pollutants. This parameter determines the hydraulic capacity, which together with the chemical properties of the filter media, affects the treatment performance of the filter system. However, measuring Ksat is time consuming and expensive. This study developed a novel transfer function to predict Ksat of coarse porous media from easily measured parameters. The hydrophysical parameters determined were Ksat, grain size distribution, bulk density, uniformity coefficient, particle density, and porosity of 46 porous media fractions. The fractions ranged in grain size from 0.5 to 20 mm and were obtained from seven commercial available coarse filter materials. A backward stepwise regression analysis was performed between Ksat and 10 variables obtained from the grain size distribution and bulk density. The optimal model for predicting Ksat contained two parameters, D20 and D50, which describe respectively the particle diameters, where 20 and 50 % of all particles are finer by weight. The predicted Ksat values were in good agreement with the measured values (R2 =0.91). The transfer function can find potential usage in relation to dimensioning of permeable E. Canga (*) : B. V. Iversen : C. Kjaergaard Department of Agroecology, Aarhus University, Blichers Allé 20, P.O. Box 50, 8830 Tjele, Denmark e-mail:
[email protected] E. Canga e-mail:
[email protected]
agricultural drainage filters or subsurface-flow constructed wetlands. The predicted values of Ksat can also be used as input to numerical models that simulate filter treatment performance. Keywords Saturated hydraulic conductivity . Predictive function . Porous filter material . Grain size distribution . Water treatment technology List of symbols Dx Grain size diameter, where x% of all particles are finer by weight UC Coefficient of uniformity, UC =D60/D10 Ksat Saturated hydraulic conductivity A Cross-sectional area q Darcy Flux Q Water discharge L Length of the column filter ΔH Hydraulic head n Number of replicates N Number of data (fractions) ρb Dry bulk density ρs Particle (solid) density θtot Total porosity
1 Introduction Porous media are used as filters that physically or biogeochemically retain nutrients and pollutants present in wastewater from different sources. Water treatment technologies that use porous media as a bed filter are
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subsurface constructed wetlands (CWs) or permeable drainage filters. The first can be horizontal or vertical subsurface CW, according to the direction of water flow through the bed filter (Vymazal 2008). The latter are innovative flow-through filter structures designed to remove dissolved phosphorus from ditch water (Penn et al. 2007; Stoner et al. 2012), from agricultural runoff (Penn et al. 2012) or from soil water by enveloping the subsurface tile drains with reactive filter materials (Buda et al. 2012; Chardon et al. 2012; McDowell et al. 2008). Differences characterizing the two types of treatment systems should be taken into consideration during the design: CWs receive relatively low and controlled volumes of wastewater from point source pollution with high concentration of suspended solids and pollutants. In opposite, the permeable drainage filters have the challenge of receiving agricultural drainage water with high hydraulic load and with extremely stochastic behavior (events of high and low water discharge), despite the low concentrations of nutrients (Penn et al. 2007). Despite these differences, there are two common requirements that every treatment system involving porous media must fulfill: the filter must have sufficient hydraulic capacity and sufficient retention/removal properties to achieve the desired discharge water quality. The fulfillment of these requirements depends directly on the hydro-physical and chemical properties of the porous media (i.e., grain size, hydraulic conductivity, affinity, etc.). Knowledge of the hydraulic capacity of the systems is crucial in relation to the dimensioning of these treatment technologies. The saturated hydraulic conductivity (Ksat) expresses the maximum water discharge of a porous media at a given hydraulic gradient and defines, therefore, the hydraulic capacity of the filter system. The Ksat depends on many factors, which Mbonimpa et al. (2002) summarized by classifying them into three groups: properties of the fluid, pore size distribution, and characteristics of the solid surface. Prior to the application of different treatment technologies, it is essential to select the proper type of filter material having the correct treatment performance and hydraulic capacity. Knowing the Ksat of a given filter material based on the above-mentioned parameters is therefore essential for the choice of an appropriate grain size of filter material for a particular water treatment technology. The challenge in selecting the appropriate grain size is that the small grains (high specific surface area) are preferred to achieve a high treatment efficiency, while large grains are preferred in order to handle the
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high hydraulic load (i.e., drainage discharge from agricultural areas). Both requirements need to be fulfilled (Arias and Brix 2005; Penn et al. 2007). The filter grain size distribution should therefore be selected based on the type of treatment technology, the type of wastewater (suspended particles entering the filter over time may decrease the porosity and therefore the Ksat), and the hydraulic load of the filter system. The high variability in drainage discharge from agricultural systems is in contrast to municipal wastewater treatment, where the hydraulic load is lower and is generally controlled. This stresses the importance of choosing a correct filter type with a suitable hydraulic capacity. The Ksat, expressing the hydraulic capacity of a given filter material, is measured either in laboratory or in situ conditions using the constant or falling head method (Klute 1965). Measuring Ksat is costly and often time consuming. It is therefore helpful to develop predictive functions for Ksat, based on easily measurable parameters of the filter media (e.g., grain size distribution). In soil science, studies to predict the Ksat of soils have been extensively conducted, using various predictors including grain size distribution (Arya et al. 2010; Boadu 2000; Carmen 1937; Iversen et al. 2011; Jabro 1992; Trani and Indraratna 2010; Vukovic and Soro 1992), bulk density (Jabro 1992), bulk density and slope of water retention curve (Rawls et al. 1998), porosity (Fallico et al. 2010), or microscopic pore geometry (Lebron et al. 1999; Schaap and Lebron 2001). However, these Ksat predictive functions for undisturbed soils can seldom be applied to the coarse filter materials used in our study, mainly due to the physical differences in the grain size distribution between soils and porous filter media. Soils are mainly finer and less sorted than the coarse filter media used in water treatment technologies. In addition, filter materials are isotropic, whereas most natural soils are anisotropic, due to the aggregation of individual soil particles. Models for predicting Ksat for the coarse filter materials used in water treatment technologies have received little attention. Studies with regard to Ksat in water treatment technologies have only focused on measuring Ksat as a function of time to assess clogging (Sanford et al. 1995) or for developing methods for in situ determination and to quantify the extent of clogging in horizontal subsurface CWs (Knowles et al. 2010). The objectives of this study were (1) to determine Ksat and the physical properties of 46 fractions originated from seven types of coarse porous filters and (2) to develop a transfer function for estimating Ksat from key
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physical parameters (bulk density, grain size, uniformity coefficient, etc.) for the entire dataset. The transfer function will be applicable to select an appropriated grain size fraction to fulfill the hydraulic requirements of a specific water treatment technology.
mixing the commercial grain size fractions of every single filter material (CDE, seashell, and limestone) with mixing ratios of 50:50, 25:75, 75:25, and 33:33:33 (weight %). A total of 46 different combinations of grain size fractions were investigated for Ksat in three replicates, resulting in a total of 138 measurements.
2 Material and Methods 2.2 Saturated Hydraulic Conductivity 2.1 Filter Materials Seven types of filter materials were selected based on their possible potential to treat drainage water (Table 1). The filter materials included three types of lightweight expanded clay aggregates which, besides the commercial product Leca (Leca®, silicate clay), included planed Leca where the surface roughness has been increased by planning (Saint-Gobain Weber A/S, Denmark) and a commercial calcium-coated Leca called Filtralite-P (Saint-Gobain Weber A/S, Norway). In addition, calcinated diatomaceous earth (CDE) material (Damolin A/S, Denmark), seashell consisting of crushed mussel shells (Danshells A/S, Denmark), limestone consisting of carbonate calcite granules (Lhoist A/S, Denmark), and CFH (ferric hydroxide granules, Kemira A/S, Finland) were used in the experiment. The filters were supplied in commercially available grain size fractions ranging from 0.5–20 mm (Table 1). To increase the number and diversity of the grain size fractions in the development of the Ksat predicting function, we included (1) commercially available grain size fractions (Table 1), (2) sieved fractions, and (3) combined grain size fractions. The sieved fractions were obtained by sieving the commercial fractions of Leca and planed Leca into new fractions of 1–2, 2–3, 3–4, 4– 8, 8–12, 12–16 mm for Leca, and 8–12, 12–16 mm for planed Leca. The combined fractions were obtained by Table 1 The filter materials involved in the study and their commercially reported grain size fractions
a
Fractions 0.7–2 and 2–5 mm are crushed shells; 5–15 mm are intact shells
Filter
Prior to the measurement of Ksat, the air-dried filter material was packed in a transparent PVC column (length = 100 cm, inner diameter = 10.4 cm). The full length of the column was used for the coarse grain size material, whereas the samples with 25 or 50-cm length were used for filter materials with fine grain size fractions (
