Mayes, Melanie A.

Parker, Jack C.

Perfect, Ed

Tang, Guoping

van den Berg, Elmer

UNT Digital Library

Coupled Processes Influencing the Transport of Uranium over Multiple ScalesGOAL: To provide validated scaling strategies which can be applied to existing contaminant distributions and migration scenarios at Hanford and similar sitesOBJECTIVES: 1. Layer Scale: Separate quantification of hydraulic, geochemical, and mineralogical factors influencing U(VI) transport2. Up-Scale: Apply numerical, composite medium, and fractal approaches to compute effective coupled hydraulic and reactive transport parameters3. Validate: Apply up-scaled parameters to U(VI) transport through progressively larger scales of intact samples that encompass both lateral and vertical U(VI) transportPROBLEM: Leaking radioactive waste has entered the subsurface at DOE sites. Prediction of contaminant transport is complicated by geological heterogeneities, resulting in scale-dependence of transport parameters.1Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, 2Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN 37996Melanie A. Mayes1 (mayesma@ornl.gov), Guoping Tang1, Jack C. Parker1, Ed Perfect2, and Elmer van den Berg2lateral (anisotropic) floweven wetting front?bypasseduneven wetting frontFlow in Heterogeneous DepositsIDF in 200EHanfordWaste storage tanks at HanfordFUTURE WORK: 1. Repeated measurements on unconsolidated granular material to determine precision of URC method.2. Determination of hydraulic properties of individual layers of large intact Hanford sediment sample.3. Determine applicability of composite medium model to transient system 4. Validate model with measurements at different scales5. Extend model from monofractal (2 materials) to multifractal (many materials)6. Extend uncertainty analysis to large-scale modelsLAYER SCALE:The ULTRA ROCK CENTRIFUGE (URC) measures water content as a function of pressure (θ(ψ)) and predicts hydraulic conductivity (K(S)). Solution is collected from centrifuged, originally saturated samples to generate a production curve (Fig. 1). The slope of the production curve is used to calculate relative permeability (Fig. 2) using the following expressions (Christiansen, 2002; Hagoort, 1980): dtdQkLk wwrw αρϕμΔ=dtdQtQS www +−= 1where μw viscosity, L length of sample, φ porosity, α average centrifugal acceleration, Δρdensity difference between displaced and invading fluid, k intrinsic permeability, krw relative permeability, Sw saturation, Qwcumulative water production, t time since centrifuge started.Fig. 2.  Relative permeability versus saturation for two small diameter Berea Sandstone test cores. The measurement was repeated 3 times.Berea Sandstone test cores were repeatedly measured to study the degree of consistency of the laboratory method (e.g., Fig. 2). At high saturations, the precision of the krwmeasurements appears to be higher than at low saturation, where the relative krw can vary up to 0.5–1.5 order of magnitude for any given saturation value.INTERMEDIATE SCALE:In order to reliably estimate transport parameters, analyses of uncertainty and sensitivity are performed to determine the contributions of model and parameter estimation errors. Previous work involved the transport of Br, Co, and U(VI) in intact Hanford sediment cores in which flow is parallel or perpendicular to bedding (Mayes et al., 2003, in prep; Pace et al., 2003, 2007). Six different parameter combinations using convective-dispersive equation (Parker and van Genuchten, 1984) for simultaneously fitting nonreactive tracer Br and reactive tracer Co are attempted (Fig. 3).   1.0E+001.0E+011.0E+021.0E+031.0E+041.0E+051.0E+061.0E+070.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40Moisture contentAnisotropyComposite dh = 10Composite dh = 100Composite dh = 1000COMA02468101.0E-12 1.0E-10 1.0E-08 1.0E-06 1.0E-04Hydraulic conductivity (cm/s)Length (cm)Layered, dh = 10Layered, dh = 100Layered, dh = 1000Composite, dh = 10Composite, dh = 100Composite, dh = 1000-1.0-0.50.00.51.01.52.02.50 1 2 3 4 5 6Pore Volumes SensitivityVelocityDispersionPulseRetardationDecay constantq = Kunsat Δh/ΔL = [L/T]LARGE 2D SCALE:Effective hydraulic parameters of unsaturated layered sediments were estimated using a physically-based Cantor Bar model to represent interbedded layers of coarse (blue) and red (fine) sediments (Tang et al., accepted).Flow crosses bedsFlow parallel to beds0.00.20.40.60.81.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Pore VolumesC/CoCofit CoLCLUCLFig. 3.  Fitting velocity (V), dispersion (D), retardation (R), pulse, and decay constant (μ) to flow-bedding-parallel Co data in Hanford Coarse (HC) sediment showing 95% confidence limits. The fit corresponds to Fit Combination #5 (Fig. 4).0.000.010.020.030.040.051 2 3 4 5 6ModelDeviationParameterModelFit Combinations1. D, R2. V, D, R3. V, D, Pulse, R4. D, R, μ (decay)5. V, D, R, μ6. V, D, Pulse, R, μFig. 4. Combined uncertainty due to model fitting error and parameter uncertainty for 6 combinations of fitting parameters. Fig. 5.  Sensitivity of fitting parameters during experimental progress.Fig. 5 demonstrates the sensitivity of parameters to the concentration measurements.1.E-131.E-111.E-091.E-071.E-051.E-031.E-011.E+010.000 0.100 0.200 0.300 0.400Moisture contentCross-bed conductivity (cm/s)Layered, dh = 10Layered, dh = 100Layered, dh = 1000CompositeComposite, dh = 10Composite, dh = 100Composite, dh = 10001.E-131.E-111.E-091.E-071.E-051.E-031.E-011.E+010.000 0.100 0.200 0.300 0.400Moisture contentParallel-bed conductivity (cm/s) Layered, dh = 10Layered, dh = 100Layered, dh = 1000CompositeComposite, dh = 10Composite, dh = 100Composite, dh = 1000Fig. 6. Comparison between layered and effective (composite) parameters at a scale of 10 cm for parallel-bed and cross-bed conductivity for a range of hydraulic gradients (dh).Fig. 7. Anisotropy as a function of gradient (dh). Fig. 8. Simulation of 2D layered system .The hydraulic conductivity calculated from layered and effectiveparameters were similar regardless of the gradient (Fig. 6). Themodel works well the for steady-state 1D case. Results were similar for length scale of 100 cm (not shown). Anisotropy is not sensitive to the gradient (Fig. 7).  0.30.40.50.60.70.80.910.01 0.1 1 10 100 1000 10000Time since start of centrifuge (min)Cumulative production (PV)Raw dataCorrected dataacceleration timeREFERENCES: Hagoort, J. (1980). Oil Recovery by Gravity Drainage. SPE. V. 20, June , p. 139-150. Christiansen, R.L. (2001). Two-Phase Flow through Porous Media. Petroleum Engineering Department, Colorado School of Mines. Pace, M.N., Mayes, M.A., Jardine, P.M., McKay, L.D, Yin, X.L., Mehlhorn, T.L., Liu, Q., and H. Gürleyük.  2007.  Transport of Sr2+ and SrEDTA2- in partially-saturated and heterogeneous sediments.  J. Contam. Hydrol. (in press). Mayes, M.A., Jardine, P.M., Mehlhorn, T.L., Bjornstad, B.N., Ladd, J.L., and Zachara, J.M.  2003.  Transport of multiple tracers in variably saturated humid region structured soils and semi-arid region laminated sediments.  Journal of Hydrology 275: 141-161.Mayes, M.A., Parker, J.C., Tang, G., Yin, X.L., McKay, L.D., and Jardine, P.M. (in prep). Anisotropy in reactive transport parameters in layered Hanford sediments during unsaturated flow. Soil Sci. Soc. Am. J. Mualem, Y. 1984. Anisotropy of unsaturated soils. Soil Sci. Soc. Am. J. 48:505-509.Pace, M.N., Mayes, M.A., Jardine, P.M., Mehlhorn, T.L., Zachara, J.M., and Bjornstad, B.N. 2003.  Quantifying the effects of small-scale heterogeneities on flow and transport in undisturbed cores from the Hanford Formation. Vadose Zone Journal 2: 664-676.Parker, J.C., and M.T.v. Genuchten. 1984. Determining transport parameters from laboratory and field tracer experiments. Bull. No. 84-3. Va. Agric. Exp. Stn., Blacksburg, VA.Tang, G., Perfect, E., van den Berg, E., Mayes, M.A., and Parker, J.C. (accepted pending revision). Estimating hydraulic parameters of unsaturated layered sediments using a Cantor Bar composite medium model. Vadose Zone. J.Yeh, T.-C., L.W. Gelhar, and A.L. Gutjahr. 1985c. Stochastic analysis of unsaturated flow in heterogeneous soils. 3. Observations and applications. Water Resour. Res. 21:465-471.1.E-071.E-051.E-031.E-010.0 0.2 0.4 0.6 0.8 1.0Saturation of wetting phase, Sw (-)Relative permeability, kwr (-)Run #1Run #2Run #3Sample 11.E-071.E-051.E-031.E-010.0 0.2 0.4 0.6 0.8 1.0Saturation of wetting phase, Sw (-)Relative permeability, kwr (-)Run #1Run #2Run #3Sample 2Fig. 1.  Production versus time at constant angular velocity of 9000 RPM. Raw data is corrected during early times in which RPM < 9000.  Fig. 4 shows that uncertainties due to model fitting errors exceed those due to parameter estimation errors.  Errors decrease with increasing estimated parameters for combinations 1-5. Combination 6, however, did not improve the fit and therefore can be eliminated. A direct averaging approach, the composite medium model, is used to scale the hydraulic parameters from individual layers to a composite system (e.g., Mualem, 1984; Yeh et al., 1985; Pruess, 2004). This approach has been criticized because it ignores variances in the hydraulic gradient (dh or ∆h) (Khaleel et al., 2002). Therefore we tested the  sensitivity of the model to variations in hydraulic gradient over scales of 10-100 cm.The variance in conductivity at high gradients causes the difference between layered and composite cases (Fig. 8). The hydraulic conductivity of the composite case is close to the harmonic mean of the layered case (Fig. 8), meaning that the composite medium approach is valid for these conditions. Funding for this project was provided by the DOE Environmental Remediation Sciences Program. Oak Ridge National Laboratory is managed by the University of Tennessee-Battelle, LLC, under contract DE-AC05-00OR22725 with the US DOE. 

Coupled Processes Influencing the Transport of Uranium over Multiple Scales

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Coupled Processes Influencing the Transport of Uranium over Multiple Scales

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