A simple solute transport model - hessd

Hydrol. Earth Syst. Sci. Discuss., 6, 5631–5664, 2009 www.hydrol-earth-syst-sci-discuss.net/6/5631/2009/ © Author(s) 2009. This work is distributed under the Creative Commons Attribution 3.0 License.

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HESSD 6, 5631–5664, 2009

A simple solute transport model M. S. Akhtar et al.

A simple two layer model for simulation of adsorbing and nonadsorbing solute transport through field soils 3 ¨ M. S. Akhtar1 , U. Mohrlok2 , and D. Stuben

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PMAS-Arid Agriculture University Rawalpindi, Rawalpindi, Pakistan Institute for Hydromechanics, University of Karlsruhe, 76131 Karlsruhe, Germany 3 Institute for Mineralogy and Geochemistry, University of Karlsruhe, 76131 Karlsruhe, Germany 2

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Received: 16 June 2009 – Accepted: 15 July 2009 – Published: 4 September 2009 Correspondence to: M. S. Akhtar ([email protected])

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Published by Copernicus Publications on behalf of the European Geosciences Union.

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While rapid movement of solutes through structured soils constitutes the risk of groundwater contamination, simulation of solute transport in field soils is challenging. A modification in an existing preferential flow model was tested using replicated Chloride and Lithium leachings carried out at constant flow rates through four soils differing in grades and type of structure. Flow rates generated by +10 mm, −10 mm, −40 mm, and −100 mm water heads at the surface of 35 cm diameter 50 cm height field columns. Three well-structured silty clay soils under ponding had concurrent breakthrough of Chloride and Lithium within a few cm of drainage, and a delayed and reduced peak concentration of Lithium with decrease in flow rate controlled by the negative heads. Massive sandy loam soil columns had delayed but uniform breakthrough of the solutes over the flow rates. Macropore flow in well-structured silty clay/clay loam soils reduced retardation, R (1.5 to 4.5) and effective porosity, θe (0.05 to 0.15), and in−1 creased macropore velocity, vm (20 to 30 cm cm drainage) compared to the massive sandy soils. The existing simple preferential flow equation (single layer) fitted the data well only when macropore flow was dominant. The modified preferential flow equations (two layers) fitted equally well both for the adsorbing and nonadsorbing solutes. The later had high goodness of fit for a large number of solute breakthroughs, and gave almost identical retardation coefficient R as that calculated by two-domain CDE. With fewer parameters, the modified preferential flow equation after testing on some rigorous model selection criteria may provide a base for future modeling of chemical transport.

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1 Introduction

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Rapid movement of solutes to tile-line may transport contaminants to groundwater and, therefore, has been studied extensively. As in field soils, retention of solutes is practically less than the determined values from the batch experiments (Hutchison et al., 5632


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2003; Akhtar et al., 2003b), the arrival time for reactive solutes is the same as that for the nonreactive solutes, e.g. pesticides (Flury et al., 1995; Kung et al., 2000), Phosphorous (Akhtar et al., 2003a), Lithium (Akhtar et al., 2003b), and other cationic and anionic metals (Huber et al., 2004; Akhtar et al., 2009). In this situation, the classical transport models fail to predict arrival time. Transport parameters are determined using the Convective-Dispersive equation (CDE) which is based on the assumption that solute front moves uniformly (Xue et al., 1997; Mohanty et al., 1998; Elliott et al., 1998; Sarmah et al., 2005). Other models with various degrees of complexity to simulate solute flow in the vadose zone have been tested, e.g. MACRO (Jarvis et al., 1991a,b); USDA’s Root Zone Water Quality Model (RZWQM) (Ahuja et al., 2000) and LEACHEM (Hutson and Wagenet, 1995). Conceptually, these models vary mainly in the amount of interaction of solutes with the soil matrix. As the validity of uniform velocity was questioned (Quisenberry et al., 1994), a tworegion mobile-immobile model where total water content is partitioned and a mass transfer function governs the mass exchange between mobile and immobile regions, addressed some of the discrepancies in modelling solute transport in field soils (Jury et al., 1991; van Genuchten, 1991). This approach has been successfully applied in many solute transport studies (Hutchison et al., 2003; McIntosh et al., 1999; Langner et al., 1999; Vervoort et al., 1999; Shaw et al., 2000). However, these models require a large number of parameters. The VS2DT (Lappala et al., 1987), requires a minimum of seven parameters (Zhang et al., 1998) which often lack physical meaning and are difficult to determine independently. Matrix and macropore flows cannot be discriminated easily, thus making hydrological characterization of the two domains uncertain (Castigione et al., 2003). In some cases erroneous parameter estimates have been reported despite high goodness of fit (Akhtar et al., 2003b; Kim et al., 2005). On the other hand, the preferential flow type equations assume that a surface layer (or a mixing layer) distributes water and solutes into the macropores of the soils’ vadose zone (Ritsema and Dekker, 1994; Steenhuis et al., 1994; Jarvis et al., 1991; Ahuja et 5633

HESSD 6, 5631–5664, 2009


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al., 2000; Kim et al., 2005). Main differences among various preferential flow models are the assumptions concerning the exchange of solutes with the soil matrix along soil pore wall. The simplest model of Steenhuis et al. (1994) assumes that the flow through the macropores is fast and no interaction takes places with the soil matrix. Other models include some interaction with the matrix (Zhang et al., 1998; Wallach and Steenhuis 1998). Ahuja et al. (2000) assume that some of the solutes end up in dead-end pores. The simple preferential flow model without interaction in the vadose zone has been found fitting only where macropore flow was dominant (Akhtar et al., 2003b). As the model assumes instantaneous mixing, it also failed when mixing and leaching processes occur simultaneously (Mahmood-ul-Hassan et al., 2003). Following the concept of “mixing” and “transport” layer (Steenhuis et al., 1994), a modified preferential flow type equation was adapted to the experimental conditions where LiCl was applied to intact soil columns at steady state flow conditions. This paper presents fits to the modified preferential flow equation, discusses the variability in the transport parameters, and compares relevant transport parameter with CDE applied with partitioning of water into mobile/immobile regions. 2 Modelling approaches

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As several approaches are referred in the literature to describe transport processes in soils with different complexity, this section summarizes the basic principles of the approaches used within this paper.

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2.1 Convective Dispersive Equation (CDE) Printer-friendly Version

The CDE model for one-dimensional transport of reactive solutes subject to adsorption in one or two domains has been solved for several boundary conditions given in Parker

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and van Genuchten (1984) and other textbooks (Marshall et al., 1996):

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∂C ∂C ∂ C R −v =D 2 ∂t ∂x ∂x

(1)

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where D is the dispersion coefficient [m s ], v=q/θ is the mean flow velocity or the transport velocity of a non-adsorbing solute [m s−1 ], respectively with the Darcy velocity q [m s−1 ] and the volumetric water content θ [m3 m−3 ]. The dimensionless retardation factor of the form

A simple solute transport model

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R =1+

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ρKa

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(2)

θ

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(Toride et al., 1999) for adsorbing solute, with a constant adsorption partitioning coef3 −1 −3 ficient Ka [m kg ] and the bulk density of solid, ρb [kg m ], scales the solute movement. Thus, the transport velocity is R times lower and arrival time R times longer compared to a non-adsorbed solute.

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2.2 Simple preferential flow model

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It describes solute transport in natural layered soils by assuming surface soil as a mixing zone and vadose zone as a conveyance zone. The mixing layer is considered as a dynamically behaving reservoir where solute sorption processes and advective transport balance. In the transport layer only a time lag to advective transport occurs. Assuming flow in the mixing zone follows linear reservoir theory, i.e. no interaction with soil matrix in the transport layer (Ritsema and Dekker, 1994) and the applied solute mixes instantaneously, the cumulative loss of solutes, L, [kg] with preferentially moving water through a soil with mixing zone of thickness d [m] is: Y (3) L = M0 1 − exp − W 5635

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(Akhtar et al., 2003b) where M0 [kg] is the initial mass applied, W =d (ρb Ka +θ) [m] is the apparent water content; and Y =qt [m] is the cumulative drainage at constant flow rate q since the time t of solute application

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2.3 Two layer preferential flow model 5

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Modification in this approach becomes necessary when a solute is injected over a certain time period T0 [s] into a water flux seeping continuously with a constant specific −1 flow rate q [m s ], a procedure corresponding to the usual tracer tests where Y0 [m] is the cumulative amount of percolation related to the application period. Then outflow concentration C1 [kg m−3 ] from mixing layer describes the mass balance within mixing layer (Fig. 1) where the solute transport is determined by advective transport and sorption processes (Eq. 4). ∂C1 d1 (θ1 + ρb Ka ) = q C0 − q C1 ∂t

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where d1 [m] is the depth. The solution of Eq. (4) for the initial condition C1 (0)=0 is split into the following two cases:

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Y 0T0 :C1 (t)=C0 1− exp − exp − Wa Wd

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The solution for 0 T2 :C2 (t) = C1 (t − T2 ) 10

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where the mean transport time T2 in transport layer is defined by: T2 =

W2 q

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The apparent water content of the transport layer depends only on the depth d2 . W2 = d2 θ2

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The overall transport is quantified by the mass leaching monitored at the system outflow by means of the outflow concentration C2 of the transport layer. Mass balance is described by calculating the deficit of the mass recovery on a logarithmic scale L(Y ) ln 1 − (10) M0

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where L(Y ) defines the mass loss from the system in terms of cumulative percolation Y L(Y ) =

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and M0 =A q C0 T0 , the total injected solute mass to cross section area A [m ] in the time interval T0 , which is defined by the observed concentration C2 (T0 )=C1 (T0 −T2 ) C1 (T1 ) W2 Wa − ln 1 − T0 = T2 + T1 = (12) q q C0 There are two calculations of the integral Eq. (11) necessary due to the two different solutions for C1 (t) (see Eq. 5), since the outflow concentration C2 (t) has to be expressed by C1 (t). This requires a time shift of T2 for the formulation of time depending function and the integration boundaries. Hence, the mass loss L(Y ) can be expressed by: 0 ≤ Y ≤ Y2 :


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L(Y ) = 0

Y2 < Y ≤ (Y0 + Y2 ) : L(Y ) = A C0 Y > (Y0 + Y2 ) :

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L(Y ) = A C0 A C0

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0 Y −Y 1 − exp − W 2 dY0

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0 Y −Y 1 − exp − W 2 d Y 0+

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0 Y Y −Y −Y 1 − exp − W0 exp − W0 2 d Y 0 . a

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Calculating the integrals in Eq. (13) and substituting into Eq. (10) gives the deficit of the mass recovery: L(Y ) 0≤Y