SOLUTE DISPERSION COEFFICIENTS IN HETEROGENEOUS POROUS MEDIA AS RELATED WITH THE MIGRATION OF PESTICIDES IN GROUNDWATER

Transcription

1 CMWRXVI SOLUTE DISPERSION COEFFICIENTS IN HETEROGENEOUS POROUS MEDIA AS RELATED WITH THE MIGRATION OF PESTICIDES IN GROUNDWATER CHRISTOS TSAKIROGLOU 1, DIMITRA TZOVOLOU 1, CHRISTOS AGGELOPOULOS 1, MARIA THEODOROPOULOU 2, THEODORA DALKARANI 2, KONSTANTINOS PIKIOS 2 1 Institute of Cheical Engineering and High Teperature Cheical Processes Foundation for Research and Technology, Stadiou str., Platani, P.O.Box 1414, GR Patras, Greece 2 Technological Educational Institute of Patras, Departent of Mechanical Engineering, Megalou Alexandrou 1, Koukouli, GR Patras, Greece ABSTRACT Breakthrough curves of iscible displaceent experients perfored on long coluns of disturbed soils are eployed to estiate the longitudinal dispersion coefficient as a function of the Peclet nuber and pore-scale heterogeneity. A 2-D nuerical siulator of the transport / sorption / biodegradation of organic copounds in porous edia is built and used to exaine the transient spreading pattern of three pesticides (glyphosate, phorate, 2,4-D) in a acroscopically heterogeneous porous ediu. The acrodispersion and flow channelling, associated with icro-scale heterogeneities, are reflected in the sall and large thickness of the acroscopic pesticide dispersion front. 1. INTRODUCTION The application of various types of pesticides to plants and soils is the ain source of diffuse pollution for groundwater. There is variety of transport processes through which the organic cheicals of pesticides igrate in the subsurface environent (Weber and Miller, 1989) such as sorption, advection, dispersion, etc. In addition, the fate of organic copounds in the subsurface is closely related with the kinetics of cheical transforation processes such as the biodegradation, abiotic hydrolysis, photocheical reactions, etc. The nuerical siulation of the transport of pesticides in underground aquifers is coplicated by the spatial and teporal variations of the physicocheical and biological characteristics of the soil (Aden et al., 2000; Stagnitti et al., 2001). For this reason, the acroscopic odeling of pesticide fate at the field scale is coonly based on assuptions (e.g. local equilibriu assuption, porous ediu hoogeneity, 1 st order kinetics of biodegradation, etc), the validation of which requires consideration of the processes at the icroscopic level (Haron et al., 1989). In spite of the great deal of attention that has been paid on the assuptions related to sorption, biodegradation, and diffusion (Bouchard et al., 1989), the hydrodynaic dispersion has been overlooked. Experiental (Theodoropoulou et al. 2003; Tsakiroglou et al., 2005) and theoretical studies (Bruderer and Bernabe, 2001) of solute dispersion pore network odels have revealed that both the longitudinal and transverse. 1

2 C. Tsakiroglou, D. Tzovolou, C. Aggelopoulos, M. Theodoropoulou, T. Dalkarani, C. Pikios dispersion coefficients (as well as the corresponding dispersivities) vary non-linearly with the Peclet nuber. One of the probles arising fro such icroscopic studies is to find out how iportant is the specific law relating the dispersion coefficient with Peclet nuber for the spreading of pesticide at the acroscopic scale. In the present work, datasets of iscible displaceent experients perfored on soil coluns are eployed to estiate the variation of the longitudinal dispersion coefficient with Peclet nuber for two soils: one with broad and another with narrow grain size distribution. These two different relationships are used as input data in a finite eleent nuerical code that siulates the sorption / biodegradation / advection / dispersion of pesticides dissolved in water in a acroscopically heterogeneous porous ediu. In this anner, the effects of the longitudinal dispersivity on the transient pattern of the pesticide spreading over the porous ediu are clarified. The nuerical code is eployed to siulate the spreading pattern of three pesticides (glyphosate, phorate, and 2,4-D) in groundwater. 2. ESTIMATION OF DISPERSION COEFFICIENTS 2.1 Miscible displaceent experients on soil coluns The longitudinal dispersion coefficient was deterined as a function of Peclet nuber by perforing iscible displaceent experients on disturbed soil coluns and onitoring the electrical conductance at 2-3 cross-sections along the colun (Aggelopoulos and Tsakiroglou, 2005). The total length of the soil colun is L =30 c and its diaeter D =5 c. Two soil saples were tested: (1) a well-sorted coercial sand (S1) with narrow grain size distribution ( D g = µ), porosity φ =0.40 and pereability k =35.8 Da; (2) a sandy soil (S2) with broad grain size distribution ( D g = µ), porosity φ =0.36 and pereability k =21.8 Da. Miscible displaceent experients of a low NaCl concentration solution by a high NaCl concentration solution were perfored on the sandy soils S1 and S2 at varying values of the Peclet nuber defined by Pe = u D D (1) p g where = q ( φa ) is the pore velocity, φ is the porosity, D is the ean grain diaeter, u p and D is the NaCl-H 2 O bulk diffusion coefficient ( D = 1.6x10 2 /s). For the soil S1 (φ =0.4, D g =200 µ) the solute concentration breakthrough curves were easured at two distances fro the colun inlet, whereas for the soil S2 (φ =0.36, D g =350 µ) the solute concentration breakthrough curves were easured at three distances fro the colun inlet (Aggelopoulos and Tsakiroglou, 2005). 2.2 Dispersion coefficients The non-linear Bayesian estiator of GREGPLUS solver of ATHENA software package was used to fit the experiental breakthrough curves to the analytic solution of the onediensional advection-dispersion equation (Tsakiroglou et al., 2005) and estiate g 9 2

3 CMWRXVI siultaneously the ean pore velocity, and the longitudinal dispersion coefficient, (Fig.1a,b). D L Dispersion coefficient, D L /D (a) Narrow grain size distribution Estiated fro experient Fitting with Eq.(3) Dispersion coefficient, D L /D (b) Broad grain size distribution Estiated fro experient Fitting with Eq.(4) Peclet nuber, Pe=<u p ><D g >/D Peclet nuber, Pe=<u p ><D g >/D FIGURE 1. Longitudinal dispersion coefficient for soil with (a) narrow grain size distribution and (b) broad grain size distribution. Concerning the soil S1, the breakthrough curves were reproduced perfectly whereas the estiated pore velocity was alost identical to its actual value calculated at each flow rate. However, we were unable to fit satisfactorily the breakthrough curves of soil S2 by using only one set of pore velocity and dispersion coefficient at a given Pe value. Because of the broad particle size distribution, the porous ediu can be regarded as a dual one with the convective-dispersive process being controlled by two pairs of paraeters. In this anner, two dispersion coefficients and two pore velocities were estiated siultaneously and were used to calculate the relationship D L ( Pe) (Fig.1b). Moreover, it is assued that at vanishing flow rates (as Pe 0 ) DL Deff, where D eff is the effective diffusion coefficient and can be calculated fro the easured values of the electrical foration factor, F and porosity (Sahii, 1995). The estiated D of soil S1 was fitted with the odel (Fig. 1a) DL D Deff D + b1 Pe + b2 L l = Pe (2) where D eff D = 0. 6 and produced the paraeter values: b 1 = 0. 88, b 2 = 0. 01, = 0. 64, l = 2.6. Respectively, the estiated D L of soil S2 was fitted with the odel (Fig.1b) DL D Deff D + b0 = Pe (3) where D eff D = 0.69, and produced the paraeter values: b 0 = 1. 46, = Given that Pe depends not only on the pore velocity but also on the average grain size, Eq.(1), it is crucial to define how these two paraeters are interrelated. It is well-known fro 1 2 epirical relationships that D g k, presuing that the porosity is kept constant.. 3

4 C. Tsakiroglou, D. Tzovolou, C. Aggelopoulos, M. Theodoropoulou, T. Dalkarani, C. Pikios Therefore, D g and k can be interrelated through the siple scaling law ( k ) 1 2 D (4) g 2 = Dg1 2 k1 3. SIMULATION OF CONTAMINANT FATE IN GROUNDWATER The steady flow of groundwater that has already been containated by dissolved organic cheicals (pesticides) and can be regarded as a iscible displaceent process where, the porous ediu is initially ( t < 0 ) occupied by an aqueous solution of solute concentration, C i = 0, and at tie t = 0, a solution of finite and constant solute concentration, C i = C0 is injected. The sorption of a pesticide on the solid surface is a strong function of the soil organic content and hydrophobicity of the solid surface and is correlated to the octanol/water partition coefficient (Eweiss et al., 1998). For the sake of siplicity we adopt the local equilibriu assuption (LEA) by considering sorption as an instantaneous process that is quantified by a distribution coefficient, K d, and retardation factor, R d given by (Haron et al. 1989) Rd = 1 + ρ g K d (5) where ρ g is the solid grain density. The biological decoposition (biodegradation) of organic copounds depends in a coplex anner on soil factors such as icrobial species and population density (Eweis et al., 1998). When icrobial bioass is optiu, it is coon to express the biological breakdown of a copound as a 1 st order reaction of the for dc dt = λc (6) where, λ is a rate coefficient that is related to the half-life tie t 1 2 by t 1 2 = ln 2 λ (7) The advection-dispersion, sorption, and biodegradation of an organic copound in a 2-D diensional porous ediu is described by the diensionless ass balance 2 C C C C C C C W Rd u u D D + ξ + ζ = ξξ + ξζ + Dξζ + D ζζ λ C τ ξ ζ ξ ξ ζ ζ ξ ζ D (8) The steady incopressible flow of a liquid with a density independent of the solute concentration is described by the continuity equation u ξ u ζ + = 0 (9) ξ ζ whereas, ignoring gravity effects, the Darcy law is written u ξ = f ( ξ ζ ), P φ ξ ( ξ ζ ) f, P u ζ = (10) φ ζ 4

5 CMWRXVI where the scalar function ( x y) f, represents the heterogeneity of a porous ediu, regarded as a spatial variation of the local pereability fro its average value k. The diensionless variables and paraeters involved in the foregoing relations are defined by 2 τ = td W ξ = x W = y W j ( W D ) u i ζ C ( C C ) ( C C ) = (11) u = i = x, y j = ξ, ζ (12) P = P k µ kl ij ( ) D D = D D i, j = x, y k, l = ξ, ζ (14) In addition, the coponents of the diensionless dispersion tensor ay be given by the approxiate relationships (Bruggean, 1999) D D D ξξ ζζ ξζ ( a W )( u + u ) + [( a a ) W ] u ( u u ) 1 2 eff D + T ξ ζ L T ξ ξ + 0 i 0 ζ (13) = D (15a) ( a W )( u + u ) + [( a a ) W ] u ( u u ) 1 2 = D (15b) eff D + T ξ ζ L T ζ ξ + ζξ 2 2 [( a a ) W ] u u ( u u ) 1 2 = D = (15c) L T ζ ξ ξ + The PDEs (8) - (10) coupled with the adequate initial and boundary conditions are solved along with the algebraic Eqs.(11)-(15) to deterine the flow and solute concentration fields over a porous ediu. 3.1 Nuerical solution of transport equations in a heterogeneous porous ediu One of the ost coon characteristics of shallow aquifers is that high pereability sand lenses ay be ebedded within an otherwise hoogeneous and low pereability soil. In order to represent such a heterogeneity, the pereability of a 2-D finite porous ediu of width W and length L is considered everywhere constant ( f ( ξ, ζ ) = 1) except for a central segent where f ( ξ, ζ ) = 10 (Fig.2a). The thickness of the porous ediu along the z-axis is 2 assued equal to its width so that flow through a total cross-sectional area A = W occurs. The lateral boundaries are ipervious, and an aqueous solution of solute concentration C = 1.0 is injected at tie τ = 0 through a single source ( ξ = 0, ζ1 ζ ζ 2 ) (Fig.2a). The aqueous solution outflows through an outlet port placed at the opposite side ( ξ = L W, ζ1 ζ ζ 2 ) of the porous ediu (Fig.2a). In order to investigate the effect of the functional for of the longitudinal dispersion coefficient (Fig.1a,b) on the pesticide transport pathways, Eqs.(8)-(10) were solved nuerically with finite eleents in the doain of the rectangular porous ediu (Fig.2a) by using the coercial FlexPDE solver, and iposing flux type boundary conditions. The paraeter values used in the siulations are given in Table 1. Τwo scenarios of heterogeneous porous edia were exained: (a) Both the low (LPR) and high (HPR) pereability regions are soils with narrow grain size distribution (NGSD); (b) Both the LPR and HPR are soils with broad grain size distribution (BGSD). Depending on the doinant soil ζ ζ. 5

6 C. Tsakiroglou, D. Tzovolou, C. Aggelopoulos, M. Theodoropoulou, T. Dalkarani, C. Pikios type, Eqs.(2)-(4) were used to calculate assued that a = 0. T D D as a function of the local Pe, whereas it was L TABLE 1. Paraeter values used in siulations Paraeter Value Paraeter Value Width, W () 1.0 Diffusion coefficient, Glyphosate : 7.9x10-10 D ( 2 /s) Phorate : 5.1x10-10 Length, L () 1.2 Sorption coefficient, K d ( 3 /kg) Pereability, k (D) Porosity, φ Inlet / outlet port, ζ 1 Ιnlet / outlet port, ζ 2 Lower & left corner of HPR, (ξ l,ζ l ) ,4-D : 6.1x10-10 Glyphosate : 61x10-3 Phorate : 18x10-3 2,4-D : 5x10-3 Half life tie, t 1/2 (s) Glyphosate : 4.06x10 6 Phorate : 5.2x10 6 2,4-D : 0.69x Octanol/water 0.55 partition coefficient, logk ow (0.3,0.4) Solubility, S (kg/ 3 ) Glyphosate : 12.0 Phorate : ,4-D : 0.62 Length of HPR, ξ h 0.5 Flow rate, q ( 3 /s) 1x10-5 Width of HPR, ζ h 0.2 Grain density, ρ g (Kg/ 3 ) 4. RESULTS AND DISCUSSION Glyphosate : -3.5 Phorate : ,4-D :2.81 (ph=1) 0.75 (ph=7) The acroscopic nuerical siulator of containant transport in a heterogeneous porous ediu was eployed to deterine the transient pattern of the spreading of several pesticides that are widely applied to agricultural cultivations of Western Greece: glyphosate, phorate, and 2,4-D. The physico-cheical properties of the pesticides (Table 1) were obtained fro literature (Bascaran et al. 1996; Halfon et al., 1996; Yu and Zhou, 2005), whereas the diffusion coefficients at dilute aqueous solutions were calculated by using the Wilke-Chang correlation (Reid et al., 1977). The solute dispersion front (SDF) is defined as the finite region within which the solute concentration changes appreciably. In both cases of NGSD and BGSD, the thickness of the SDF is relatively sall in the LPR (Fig.3a-d) wherever the flow velocity is negligible and solute transport is controlled by diffusion (Fig.2b,c), or the flow velocity is finite (Fig.2b,c) but still so sall ( D L Pe ) that solute transport is controlled by acrodispersion (Tsakiroglou et al., 2005). However, the SDF widens over the HPR (Fig.3a-d) where the flow velocity and Pe increase sharply (Fig.2b,c). In the NGSD, at high flow velocities, solute transport is controlled 2 by flow channelling (Taylor dispersion, D L Pe ) which norally leads to a wide solute concentration profile (Tsakiroglou et al., 2005) so that the thickness of SDF increases significantly (Fig.3a,c). Regarding the NGSD, the SDF becoes wide not only over the HPR 6

7 CMWRXVI but also over the LPR (Fig.3a,c), given that Pe increases at the vicinity of the outlet port (Fig.2b) as well. However, in the BGSD, acro-dispersion reains the doinant transport echanis ( D L Pe ) even at high Pe values, with result that the thickness of the SDF (Fig.3b,d) is saller than that observed in the NGSD (Fig.3a,c). These different pesticide spreading patterns in the two porous edia (one with NGSD and one with BGSD) essentially arise fro the different icroscopic heterogeneity of the two edia. In the NGSD porous ediu, the spatial variation of the pore sizes is quite sall and at increasing flow velocities, solute olecules follow the high velocity strealines (flow channeling, Fig.1a). Instead, in the BGSD porous ediu, the spatial variation of the pore sizes is very large and only interconnected clusters of large pores (critical paths) contribute substantially to both flow and dispersion (acro-dispersion, Fig.1b). The aforeentioned phenoena becoe ore evident for pesticide 2,4-D, where the retardation factor is sall enough, and the average pesticide velocity ( u p R ) is closer to the pore velocity (Fig.3c,d). d (a) (b) (c) ξ h ζ 2 -ζ 1 ζ h w ξ l ζ 1 ζl L FIGURE 2. (a) Geoetry of the 2-D porous ediu. (b) Spatial distribution of the Peclet nuber over a porous ediu having NGSD. (c) Spatial distribution of the Peclet nuber over a porous ediu having BGSD. (a) (b) (c) (d) τ=1.1x10-4 τ=1.1x10-4 τ=7x10-6 τ=7x10-6 τ=1.5x10-4 τ=1.5x10-4 τ=1.2x10-5 τ=1.2x10-5 FIGURE 3. Siulated transient pesticide concentration profiles within the porous ediu: Transient pattern of glyphosate spreading when both the LPR and HPR have (a) NGSD, and (b) BGSD. Transient pattern of 2,4-D spreading when both the LPR and HPR have (c) NGSD, and (d) BGSD.. 7

8 C. Tsakiroglou, D. Tzovolou, C. Aggelopoulos, M. Theodoropoulou, T. Dalkarani, C. Pikios The foregoing analysis revealed that the functional for of the dispersion coefficient, associated with icroscopic heterogeneities and coonly overlooked in acroscopic siulations, is of key iportance for predicting the pattern of pesticide spreading in aquifers. ACKNOWLEDGEMENTS This work was funded by the Greek Ministry of National Education and Religious Affairs under EPEAEK II ARCHIMIDES, Key-action: Strengthening research groups of TEI in subjects of environent and ecology, Sub-project: Developent of ethodologies for the detection of pesticides in soils and groundwater, used as tools for the risk assessent of the diffuse pollution in the environent AFYDATWSH REFERENCES 1. Aden, K., and B. Diekkruger (2000), Modeling pesticide dynaics of four different sites using the odel syste SIMULAT, Agricultural Water Manageent, 44, Aggelopoulos, C. and C.D. Tsakiroglou (2005), Siultaneous deterination of the two-phase flow and hydrodynaic dispersion coefficients of soils fro transient iiscible and icible displaceent experients, Paper SCA , Proceed. of the 2005 International Syposiu of the Society of Core Analysts, August 21-25, 2005, Toronto, Canada. 3. Baskaran, S., N.S. Bolan, A. Rahan, and R.W. Tillan (1996), Pesticide sorption by allophonic and non-allophanic soils of New Zealand, New Zealand J. of Agricult. Research, 39, Bouchard, D.C., C.G. Enfield, and M.D. Piwoni (1989), Transport processes involving organic cheicals, In: Reactions and Moveent of Organic Cheicals in Soils, B.L. Sawhney and K. Brown (eds), Soil Science Society of Aerica, Madison, Wisconsin, USA. 5. Bruggean, G.A., Analytical Solutions of Geohydrological Probles, Elsevier, Asterda, Bruderer, C., and Y. Bernabe (2001), Network odelling of dispersion: transition fro Taylor dispersion in hoogeneous networks to echanical dispersion in very heterogeneous ones, Water Resour. Res., 37, Eweiss, J.B., S.J. Ergas, D.P.Y. Chang, and E.D. Schroeder (1998), Bioreediation principles, McGraw-Hill, NY, USA. 8. Halfon, E., S. Galassi, R. Bruggeann, and A. Provini (1996), Selection of priority properties to assess environental hazard of pesticides, Cheosphere, 33, Haron, T.C., W.P. Ball, and P.V. Roberts (1989), Nonequilibriu transport of organic containants in groundwater, In: Reactions and Moveent of Organic Cheicals in Soils, B.L. Sawhney and K. Brown (eds), Soil Science Society of Aerica, Madison, Wisconsin, USA. 10. Reid, R.C., J.M. Prausnitz, and T.K. Sherwood (1977), The properties of gases and liquids, McGraw- Hill, NY. 11. Sahii M. (1995), Flow and Transport in Porous Media and Fractured Rock: Fro Classical Methods to Modern Approaches, VCH, Weinhei, Gerany. 12. Stagnitti, F., L. Li, A. Barry, G. Allinson, J.-Y. Parlange, T. Steenhaus, and E. Lakshanan (2001), Modeling solute transport in structured soils: perforance evaluation of the ADR and TRM odels, Matheatical and Coputer Modeling, 34, Theodoropoulou, M., V. Karoutsos, C. Kaspiris, and C.D. Tsakiroglou (2003), A new visualization technique for the study of solute dispersion in odel porous edia, J. Hydrology, 274, Tsakiroglou, C.D., M.A. Theodoropoulou, V. Karoutsos, and D. Papanicolaou (2005), Deterination of the effective transport coefficients of pore networks fro transient iiscible displaceent experients, Water Resour. Res., 41, W Weber, J.B., and C.T. Miller (1989), Organic cheical oveent over and through soil, In: Reactions and Moveent of Organic Cheicals in Soils, B.L. Sawhney and K. Brown (eds), Soil Science Society of Aerica, Madison, Wisconsin, USA. 16. Yu, Y., and Q.X. Zhou (2005), Adsorption characteristics of pesticides ethaidophos and glyphosate by two soils, Cheosphere, 58,