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Diffusion Coefficients and Hydraulic Conductivity in Unsaturated Hanford Soils and Sediments

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Diffusion Coefficients and Hydraulic Conductivity in Unsaturated Hanford Soils and Sediments TA 0 08125 DIFFUSION COEFFICIENTS AND HYDRAULIC CONDUCTIVITY IN UNSATURATED HANFORD SOILS AND SEDIMENTS J. V. Wright January 1990 Presented at the First Annual International High-Level Radioactive Waste Management Conference April 8-12, 1990 Las Vegas, Nevada Work supported by the U.S. Department of Energy under Contract DE-AC06-76RLO 1830 Pacific Northwest Laboratory Richland, Washington 99352 DIFFUSION COEFFICIENTS AND HYDRAULIC CONDUCTIVITY IN UNSATURATED HANFORD SOILS AND SEDIMENTS JUDITH WRIGHT Pacific Northwest Laboratory Box 999, Mail Stop KG-84 Richland, Washington 99352 (509) 376-7915 ABSTRACT unsaturated transport parameters that are poorly known but that are key input parameters to existing Two groundwater transport parameters of some and developing models of contaminant release from Hanford formation materials, the hydraulic repository systems.1,2 Knowledge of D and K as conductivity and the diffusion coefficient, were functions of the volumetric water content, B, is measured to aid in predicting contaminant migration. particularly important in the near-field transition he hydraulic conductivities and diffusion zone around waste packages where changes in coefficients for five soil types were determined as temperature, water content, compaction of backfill, ,._functions of the water content for the aqueous infiltration of fines, and secondary mineralization Rhase. The degree of saturation (or the volumetric will alter the transport character of near-field water content) in the soil was fixed at desired environments. This study experimentally evels by use of a high-speed core ultracentrifuge determined the diffusion coefficient and hydraulic with an ultralow constant-rate flow pump feeding conductivity of five subunits of the Hanford ' water into the sample through a rotating seal. formation at various degrees of saturati~n for use ,· fter the water content was fixed and the soil was in modelling of subsurface flow and transport at the at hydraulic steady-state (within two to four site. In addition, preliminary results are reported ho urs), the electrical conductivity was measured for unsaturated retardation factors for potassium u ing a 1 kHz conductivity bridge. Diffusion ion in three different Hanford soils. 'coefficient values · were calculated from the measured electrical conductivity values using the Traditional methods of investigating unsaturated Nernst-Einstein equation. Hanford formation soils systems require very long times to attain !x hibit great heterogeneity regarding hydraulic homogeneous distributions of water because normal onductivity in subunit soils. Hydraulic gravity does not provide a large enough driving conductivity ranged from 1 o· 7 cm/sec to 1 o· 4 force relative to the low hydraulic conductivities cm/sec depending on soil type and water content. that characterize highly unsaturated conditions. An However, diffusion coefficients depended only on unsaturated flow apparatus (UFA™) has been water content, although water content is controlled developed in which hydraulic steady-state can be by the hydraulic properties of each soil under achieved rapidly in most geologic materials at similar hydrologic conditions. Diffusion coefficients volumetric water contents as low as 0.5%. Soil ranged from 1 o-8 cm2/sec at volumetric water samples were placed in the UFA™ to achieve contents between about 3% and 5% to hydraulic steady-state with 0.1 M KCI as an 1 o-6 cm 2/sec at volumetric water contents electrolyte solution. The diffusion coefficient between 15% and 25%. corrected to infinite dilution was determined f ram the measured electrical conductivity (EC) of the INTRODUCTION sample using the Nernst-Einstein equation. This method is subsequently referred to as the UFA-EC Modelling the transport of contaminants in method and is also described elsewhere in this vadose zones surrounding nuclear and hazardous volume (Conca, "Diffusion Barrier Transport waste repositories requires knowledge of the Properties of Unsaturated Paintbrush Tuff Rubble material characteristics under unsaturated Backfill"). conditions. The diffusion coefficient, D, and hydraulic conductivity, K, are two of several EXPERIMENT AL METHODS solutions4,5 and was developed for this study using a variation of the two-electrode method.6 The UFA™ developed for this study consists of a rock core ultracentrifuge with an ultralow constant­ The electrical conductivity cell designed for use rate flow pump which provides fluid to the sample in the UFA™ fits inside the centrifuge sample surface through a rotating seal assembly and chamber. Two stainless steel ring electrodes microdispersal system. A centripetal acceleration 2.5 cm apart maximize contact area with the soil. (or its inertial effect, the centrifugal field) is a Stainless steel electrodes are ideal for the water body force like gravity, and so acts simultaneously contents and the current densities used in these over the entire system and independently of other experiments (~1 mNcm2).7 driving forces, e.g., gravity or matric suction, and does not induce significant changes in the sample After electrical conductivity measurements are packing, density or other physical properties.3 made, they can be related to the diffusion Accelerations up to 20,000 g are attainable at coefficient through the Nernst-Einstein equation.8 temperatures up to 1 so°C and flow rates as low For the experimental design of this study, the as 0.1 ml/hr. Effluent is collected in a Nernst-Einstein equation is transparent, volumetrically-calibrated container at the bottom of the sample assembly. Effluent D; = RT . X fil2!; (2) collection can be observed and recorded during F2 Z;C; centrifugation through a window in the sample assembly using a strobe light. where Di is the diffusion coefficient of the ith ion Under a centripetal acceleration in which the (cm2/sec), R is the gas constant (J/deg mol), Tis _water is driven by both the matric potential and .the absolute temperature (Kelvin), Fis Faraday's centrifugal force per unit volume, pro2 r, Darcy's constant (coul/mol), 8 is the cell constant for the aw is given by UFA™ conductivity cell sample holder (cm-1 ), G is the measured conductance on the conductivity bridge q = -K(l/f) {dl/f/dr - pm2rj ( 1) (mhos), ti is the transport or transference number of the ith ion (tK+ = 0.4898; 0.1 M), Zi is the charge - here q is the flux density into the sample; K is the number on the ith ion · (dimensionless) and C; is the 'hydraulic conductivity, which is a function of the molar concentration of the ith ion. The diffusion atric suction (y,) and therefore of water content coefficients determined in this study have been 'f)); r is the radius from the axis of rotation; p is the corrected for solution non-ideality using the fluid density; and w is the rotation speed (rad/s). extended Debye-H0ckel approximation.9 he system reaches steady-state in soils in two to four hours. Moisture distributions in soil samples VERIFICATION OF THE UFA-EC TECHNIQUE prepared in the UFATM are uniform to within at least 3%. Appropriate values of rotation speed and flow Diffusion coefficient values for Hanford soils rate into the sample are chosen to obtain desired were determined using the UFA-EC technique. These values of flux density, water content, and hydraulic values were compared to results from previous conductivity within the sample. At speeds above studies on similar soils verifying that the UFA-EC about 400 rpm, provided that a sufficient flux technique is valid and compares favorably with density exists, dy,/dr .. p w2 r and, therefore, traditional techniques for determining diffusion equation (1) is reduced to q = K(y,) [p ro 2 r] or coefficients . K(y,) = qlpw2r. As an example, a 45-gram sample of a silt accelerated to 2000 rpm with a flow rate An empirical relationship was developed by into the silt of 3 ml/hr achieved hydraulic steady­ Kemper and others to describe diffusion coefficients state in two hours at a volumetric water content of as a function of water content and soil type.1 o, 11 22.4% and an unsaturated hydraulic conductivity of This relationship illustrated that the solute diffusion 2.5 x 10-7 cm/sec. coefficient, D, is a positive exponential function of water content, e, and is independent of solution ionic Electrical conductivity in a potentiostatic or strength below about 1 M. The relationship is: galvanostatic mode provides reliable estimates of diffusion coefficients in dilute electrolyte so-.-------------------- 40 -(.) a.> Cl) - 30 E (.) ,..._ 20 Hanford G-1 soil pristine 1.37 glee 0.1 M KCI pa 0(8). D*ae 0 10 P • 10 a• 0.005' o· .. o.00002s em2/s 1.4 glee 0 0 1 0 2 0 3 0 4 0 Volumetric Water Content (%) Figure 1. Comparison of diffusion coefficients for . the Hanford G-1 soil determined by the UFA-EC method (open circles) and from the literature empirical relationship (closed circles). The regression curve has an R = 0.99. ' D(e) = D*aeb0 (3) diffusion coefficients in the soils determined by the UFA-EC technique are valid. where D* is the free diffusion coefficient in a pure­ water system, and a and b are empirical constants In the absence of ptiysicochemical processes, determined from experimental results by traditional simple diffusion coefficients are similar for all ionic techniques 12. Olsen and Kemper11 reported that aqueous species, differing by, at most, a factor of data for soils fit this relationship if b = 1 O and a four. This simple diffusion coefficient is what . the varies from 0.005 to 0.001 depending on soil type electrical conductivity method measures. Numer­ and texture (sand to clay, respectively). ical models using 0(0) as an input parameter require the simple diffusion coefficient, as measured by the Diffusion coefficients for potassium ion in the UFA-EC method, which can differ from 0(0) ·· Hanford G-1 soil obtained using the UFA-EC measured from traditional half-cell methods.
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