Simulating environmental tracer transport in unsaturated-saturated porous media

Transcription

1 38 Caibration and Reiabiity in Groundwater Modeing: From Uncertainty to Decision Making (Proceedings of ModeCARE 25, The Hague, The Netherands, June 25). IAHS Pub. 34, 26. Simuating environmenta tracer transport in unsaturated-saturated porous media G. A. ONNIS 1, R. ALTHAUS 2, S. KLUMP 3, H. J. W. M. HENDRICKS FRANSSEN 1, F. STAUFFER 1 & W. KINZELBACH 1 1 Institut of Hydromechanics and Water Resources Management, ETH-Hönggerberg, CH-893 Zürich, Switzerand onnis@ihw.baug.ethz.ch 2 Cimate and Environmenta Physics Division,University of Bern, CH-312 Bern, Switzerand 3 Department of Water Resources and Drinking Water, EAWAG, CH-86 Dübendorf, Switzerand Abstract Environmenta tracers have been reeased to the atmosphere by human activities since the eary 195s. They provide a powerfu too for investigations of subsurface dynamics, in particuar for the determination of groundwater residence times. When considering deep groundwater tabes (>1 m beow surface), the unsaturated zone transport of these tracers becomes a key issue for the correct evauation of the groundwater age. Deays of more than 1 years can occur in crossing the vadose zone. In the present work we investigate the subsurface dynamics of four different environmenta tracers, 3 H, 3 He, 85 Kr and SF 6, with particuar emphasis on the tracer transport in the unsaturated zone. The method deveoped is appied to the Batenswi aquifer (Switzerand). Keywords environmenta tracers; groundwater; groundwater age dating; transport; unsaturated zone INTRODUCTION Since the eary 195s, human activities such as nucear power production, thermonucear bomb testing, and industria processes have reeased increasing amounts of a range of environmenta tracers into the atmosphere. Many of these tracers are soube in water, thus providing an important too with which to track water movement in the hydroogica cyce. The atmospheric concentrations of these tracers have been measured at reference sites over the ast decades. By measuring the concentrations in groundwater and comparing the measured vaues with the known atmospheric growth curve (caed the atmospheric input function) it is possibe to determine the groundwater age. When considering thick unsaturated zones, the time spent by the tracer in the unsaturated zone resuts in a time ag or deay that must be considered in the cacuation of the groundwater age. For water tabes at a depth of ess than 1 m beow the surface, this effect is amost negigibe, but it gains in importance as deeper water tabes are considered. It was shown (Cook & Soomon, 1995) that the time ag for a 3 m water tabe depth can range between 8 and 15 years. Crossing the unsaturated zone aso resuts in a modification of the tempora concentration distributions of the tracers. The shape of the input function at the groundwater tabe differs significanty

2 Simuating environmenta tracer transport in unsaturated-saturated porous media 39 from that of the atmospheric input function. Consequenty, the concentration history at the bottom of the unsaturated zone must be reconstructed to give a correct input function for any meaningfu transport modeing in the saturated zone. We investigate the transport of the tracers 3 H, 3 He (decay product of 3 H), 85 Kr and SF 6 in the unsaturated zone by means of a numerica soution to the vertica advection dispersion equation. Considering different tracers has the advantage of taking into account the different transport mechanisms in the subsurface. Tracer transport in the subsurface can occur both in the iquid and gas phases. The water bound tracer 3 H moves by advection foowing the seepage water, whie the transport of the gas tracers ike 3 He, 85 Kr and SF 6 is advection dominated ony in the few upper metres of the unsaturated zone, whie afterwards they are diffusion dominated. We appy our theoretica studies to the Batenswi aquifer (Switzerand). The catchment of this reference site was seected as it has been reativey we studied in the ast decade. The unduating topography of the site a sandy-grave formation formed in the Riss ice-age gives rise to a compicated unsaturated zone geometry that makes Batenswi a chaenging test site for the vaidation of our unsaturated/saturated zone transport mode. TRACER TRANSPORT IN THE UNSATURATED ZONE Theory We consider the advection dispersion equation in the unsaturated zone for radioactive tracers as derived by Cook and Soomon (1995): 2 ( θ cg ) cg c g = D q θ 2 t z z λc where c g (z,t) is the gas concentration as a function of depth z and time t and: θ = ε + θρ K + (1 θ ε ) ρ K K D a = D g w + D ρ K q = q 1 ρ K + q W g W a s W g d are the effective parameters describing the soi and tracer physica properties: water content θ, gas fied porosity ε a, iquid and soid phase density ρ and ρ s (g m -3 ), decay constant λ (year -1 ), water/gas and soid/iquid partitioning coefficients K w and K d, effective iquid and gas diffusion coefficients D and D g (m 2 year -1 ), mean iquid and gas fuxes q and q g (m year -1 ). We assume: 1. Constant vaues for the physica parameters describing the unsaturated zone structure: ε a =.15, θ =.1, n = Soubiity equiibrium at the surface between atmospheric and soi water and gas tracer concentration. Water/air partitioning coefficient: K w =.1 for a gas tracers H is bound to the water moecue: K w = 1 for tritium. 4. Negigibe sorption. Soid/water partitioning coefficient: K d =.

3 4 G. A. Onnis et a. 5. Advection of the gas phase is important ony in the first upper metres of the unsaturated zone: q g =. Ony for tritium 3 H, is advection of the iquid phase the driving transport phenomenon: q =.83 m year -1. With these assumptions, the transport phenomena are controed by the foowing parameters: 3 He, 85 Kr, SF 3 6 H θ ε a θ θρ K w D D g = D g τgεa D = D ρ K = q q ρ w q = 1 KW where D g and D are the diffusion coefficients in free air and water, respectivey, and τ g is the gas phase tortuosity (constant τ g =.25 is assumed). The one-dimensiona (1-D) numerica soution to the advection dispersion equation is obtained by a forward-time and centra-space finite difference scheme. The conjugate gradient sover is used to get the soution of the impicit system. The unsaturated zone is modeed as an N-ce homogeneous 1-D coumn with the upper boundary at constant concentration (equa to the atmospheric one) and a ower boundary at depth z (z being spatiay variabe) with a constant outgoing fux (equa to the average groundwater recharge rate, r = 633 mm year -1 ). For the actua recharge rate vaue, diffusion at the ower boundary is not considered (it may, however, become important in ow recharge conditions). Resuts Simuations were performed for 85 Kr (D g = 44 m 2 year -1, haf-ife τ 1/2 = 1.76 years) and SF 6 (D g = 26 m 2 year -1 ), respectivey, making use of the Freiburg am Breisgau (Germany) input function for 85 Kr and the goba input function for SF 6 (data from IAEA, Internationa Atomic Energy Agency). The concentration profies at different depths foow the atmospheric input function (soi surface profie), but become smoother and ose detai with increasing depth. A time deay is aso apparent in the shift to the right of the concentration profies as depth increases (Fig. 1). Sensitivity anaysis shows no apparent dependence of the concentration profies on either water content, θ, or on gas fied porosity, ε a, (constrained by n = θ + ε a ). A remarkabe sensitivity is found with respect to gas phase tortuosity, τ g, raising tortuosity (and thus the effective diffusion coefficient) resuts in higher concentration vaues at depth, i.e. in faster tracer dynamics in the subsurface. As expected, sensitivity to the depth of the ower boundary is aso important: the deeper the boundary, the sower the tracer dynamics. This consideration is of major importance when considering aquifers with overying unduating topography, i.e. variabe unsaturated zone thickness. Smaer sensitivity is found with respect to the recharge rate which enters the mode as the constant outgoing fux at the ower boundary.

4 Simuating environmenta tracer transport in unsaturated-saturated porous media 41 Concentration [dpm/cckr] soi surface 1 mt. 2 mt. 3 mt. 4 mt. 5 mt. 85 Kr input function c(z,t) Concentration [pptv] soi surface 1 mt. 2 mt. 3 mt. 4 mt. 5 mt. SF 6 input function c(z,t) Year Year Fig Kr (years ) and SF 6 (years ) time series for different depths of the unsaturated zone. Simuations for 3 H (D =.495 m 2 year -1, haf-ife τ 1/2 = years) and 3 He (D g = 2179 m 2 year -1 ) as its stabe daughter product were performed, making use of the Konstanz (Germany) 3 H input function (Fig. 2). 3 H input function c(z,t) 3 He input function c(z,t) 1 8 soi surface 1 mt. 2 mt. 3 mt. 4 mt. 5 mt mt. 2 mt. 3 mt. 4 mt. 5 mt. Concentration [TU] 6 4 Concentration [TU] Year Year Fig. 2 3 H and 3 He (years ) time series for different depths of the unsaturated zone. Longitudina dispersivity is set equa to α L = 5 m. The upper boundary condition for 3 He transport simuation is TU (atmospheric concentration). The advective character of the 3 H transport equation resuts in a sharp and ess smoothed shift to the right of the concentration profies (deay effect). This expains the faster 3 H transport dynamics compared to other environmenta tracers, which is controed by the advection term parameter. Some sensitivity of 3 H and 3 He concentration profies to water content θ and gas fied porosity ε a is found, as we as to mean water fux q : higher water content (and thus ower gas fied porosity) resuts in sower dynamics of both 3 H and 3 He. Sensitivity to gas phase tortuosity τ g is again found to be the most reevant. Some sensitivity to recharge rate as we as to the depth z of the ower boundary is aso found for both tracers.

5 42 G. A. Onnis et a. CASE STUDY: UNSATURATED AND SATURATED ZONE TRANSPORT IN THE BALTENSWIL AQUIFER The Batenswi (Kanton Zürich, Switzerand) aquifer is part of the Aatha aquifer, a sandy-grave formation mainy formed in the Riss ice-age. The highy conductive ayer is covered by moraine deposits and is underain by poory permeabe sity and oamy ake deposits. Parts of the catchment are situated competey in the more or ess permeabe moraine ayer, underain by the impermeabe rock formation. The thickness of the unsaturated zone varies between and 5 m. The domain (3 3 km 2 ) is divided into two aquifer zones for modeing purposes (Fig. 3): a arge saturated domain, characterized by a stochastic transmissivity fied (T = 1-3 m 2 s -1 on average) and a second smaer infow area (indicated with arrows, northeast of the arger area) is modeed as a very thin aquifer with ow constant transmissivity (T = 1-4 m 2 s -1 ). The second area is defined in order to account for the inputs from the unsaturated zone ying above it, which consequenty become the boundary fuxes of environmenta tracer to the aquifer proper. Fig. 3 Borehoes and measuring points for Batenswi aquifer.

6 Simuating environmenta tracer transport in unsaturated-saturated porous media 43 Saturated zone stochastic fow mode The fow mode for the saturated zone is based on a set of 1 mutipe equay-ikey reaizations of the og-transmissivity fied generated with GCOSIM3D (Gómez- Hernández & Journe, 1993) conditiona to transmissivity (T) measurements. In addition, these ogt fieds are aso conditioned to steady-state hydrauic head measurements by the Sequentia Sef-Caibrated Method (Gomez-Hernández et a., 1997a,b), impemented in the code INVERTO (Hendricks Franssen, 21). Transport mode For each ce of the domain (6 6 ces) we sove the transport equation in the unsaturated zone for a 1-D coumn with the ower boundary set at a depth equa to the unsaturated zone thickness, previousy cacuated by means of the difference between the atitude a.m.s.. (from a Digita Eevation Mode) and the cacuated ensembe average hydrauic head (Fig. 4, bottom right). According to the unduating topography of the site and given the atmospheric input function, we reconstruct the concentration history at the bottom of the unsaturated zone. This was then used as concentration input fux for transport modeing in the saturated zone (performed with MT3DMS (Zheng, 199)) for the years For transport simuations in the saturated zone, we use a fow mode based on one transmissivity reaization drawn from the ensembe. Fig. 4 Two stochastic transmissivity reaizations (top-eft and top-centre) and reated hydrauic head fieds (bottom-eft and bottom-centre) from the 1 reaizations set. On the right-hand side, average transmissivity (top-right) and average head (bottom-right) fieds over 1 reaizations.

7 44 G. A. Onnis et a. RESULTS Breakthrough curves at the Batenswi pumping station show on the whoe a fair simutaneous match between simuated and measured concentrations (Fig. 5). Fig. 5 Breakthrough curves at the Batenswi pumping stations for the four different tracers. Sensitivity anaysis on the fina breakthrough curves at the measuring ocations shows that the mismatch between cacuated and simuated vaues can be reduced with proper parameter caibration, the most important being the atmospheric input function. Due to its very oca character ( 3 H especiay is sti often used in industria activities), the input function is the most uncertain input parameter of the mode. Aso the unsaturated zone transport parameters, such as gas tortuosity (effective diffusion coefficient), recharge rate and water content (for the 3 H and 3 He simuations) pay an important roe on the fina breakthrough curves. Saturated zone transport has aso been performed making use of different fow modes based on different transmissivity reaizations from the stochastic ensembe (Fig. 4), transmissivity being usuay the most important parameter affecting the mode predictions uncertainty. No sensitivity to the transmissivity reaization has been found because of the short residence times in the saturated zone. In shaow aquifers the most important roe for the transport mode caibration is then payed by the unsaturated zone dynamics.

8 Simuating environmenta tracer transport in unsaturated-saturated porous media 45 CONCLUSIONS The tracer dynamics in the unsaturated and saturated zone for the radioactive gas tracers 85 Kr, SF 6, 3 He (stabe), and water bound 3 H have been investigated. The concentration profies in the subsurface differ significanty from the atmospheric input function, even in a 1-D and homogenous medium. In the rea word, heterogeneity and negected 2-D/3-D effects wi pay an important roe in the modification of the input function at the groundwater tabe. Different transport dynamics in the unsaturated zone are recognized as the most important factor in determining the tracer concentrations at the groundwater tabe. Where groundwater is recharged through a thick unsaturated zone, and especiay in areas where topography is unduating, it is necessary to reconstruct the tracer input at the interface between unsaturated and saturated zone. Sensitivity anaysis showed the major importance of parameters such as the input function and the effective diffusion coefficients. Transport mode resuts are most sensitive with respect to eventuay heterogeneous parameters describing the unsaturated zone. The next step after this study woud be the stochastic modeing of these parameters in order to set the modeing probem in an uncertainty assessment context. Acknowedgements The project is supported by the Swiss Nationa Science Foundation (SNF), Project no /1. REFERENCES Cook, P. G. & Soomon, D. K. (1995) Transport of atmospheric trace gases to the water tabe: impications for groundwater dating with chorofuorocarbons and krypton 85. Water Resour. Res. 31(2), Gómez-Hernández, J. J. & Journe, A. G. (1993) Joint simuation of mutigaussian random variabes. In: Geostatistics Troia 92, vo. I (ed. by A. Soares), 85 94, Kuwer Academic Pubisher, Dordrecht, The Netherands. Gómez-Hernández, J. J., Sahuquio, A. & Capia, J. E. (1997a) Stochastic simuation of transmissivity fieds conditiona to both transmissivity and piezometric data. I. Theory. J. Hydro. 23, Gómez-Hernández, J. J., Sahuquio, A. & Capia, J. E. (1997b) Stochastic simuation of transmissivity fieds conditiona to both transmissivity and piezometric data. II. Demonstration on a synthetic aquifer. J. Hydro. 23, Hendricks Franssen, H. J. W. M. (21) Inverse stochastic modeing of groundwater fow and mass transport. PhD Thesis, Technica University of Vaencia, Spain. IAEA (25) Isotope Hydroogy Information System (ISOHIS), Internationa Atomic Energy Agency (IAEA), Vienna, Austria. Zheng, C. (199) MT3D, A moduar three-dimensiona transport mode for simuation of advection, dispersion and chemica reaction of contaminants in groundwater systems. Report to US Environmenta Protection Agency. S.S. Padadopuos and Associates, Inc., Rockvie, Maryand, USA.