Retardation factors, R_f, can be determined in flow experiments where R_f for a particular species is the ratio of the solution velocity to the contaminant velocity. The retardation factor for that species is given by( Bouwer, H. 1991.Ground Water, 29:41-46.)

where V_gw is the velocity of the water and V_sp is the velocity of the contaminant species. This is a bulk property that describes the overall migration of the chemical species with respect to the water and can be thought of as a chemical front moving somewhere behind the water front, but retarded by the various chemical interactions (Figure 1). If none of a particular species is retarded then R_f = 1 and the contaminant travels along with the water at the groundwater flow rate. When Rf are large, as for plutonium (R_f > 10⁴ in most soils) the contaminant can take many years to migrate offsite. Because R_f describes the chemical behavior, it depends upon any factor strongly affecting chemistry, e.g., temperature, pH, redox potential, salinity, organic content, and concentrations of other chemical species. Each chemical species has its own R_f which changes as the chemistry changes. This complexity has resulted in unsuccessful predictions of retardation factors from general principles. R_f must be measured experimentally for each species under each condition for each system. Because this can be time consuming, batch tests have traditionally been performed to measure the distribution coefficient, K_d, where one part solid is placed into ten parts solution and shaken for 24 or 48 hours to observe the amount that is sorbed onto the solid. K_d can be used to estimate R_f by( Bouwer, H. 1991.Ground Water, 29:41-46.)

R_f = 1 + K_d/n

where is the dry bulk density and n is the porosity. But for most subsurface conditions, batch experiments do not reproduce behavior in the field and can overestimate the retardation of soils and rocks. It is better to perform column experiments using the actual soil or rock, groundwater and contaminants under field conditions. In column experiments, contaminated groundwater is pumped into a column of soil packed to field density. The effluent from the column is monitored for the contaminant of interest. A breakthrough curve is obtained for the particular contaminant and R_f is determined as the pore volume at which the concentration of the chemical species exiting the sample is 50% of the entering solution, or C/C_o = 0.5. However, under unsaturated conditions or in very low permeability materials these experiments can take years because of low flow rates. Pressure systems cannot be used for unsaturated conditions and can cause significant chemistry changes in pressure-sensitive phases such as calcite, clay minerals, or gypsum.

Figure 1

The UFA method can be used to reduce these times dramatically by allowing flow rates to increase and by being able to target the desired water content or permeability of the system and reach hydraulic steady-state in hours.( Lindenmeier, C. W., R. J. Serne, J. L. Conca, A. T. Owen, and M. I. Wood 1995. Technical Report PNL-10722, Pacific Northwest Labs, Richland, WA.) The UFA achieves steady-state in any porous media by using an adjustable, whole-body driving force together with precision flow. The UFA instrument consists of an ultra-centrifuge with a constant, ultralow flow pump that provides fluid to the sample surface through a rotating seal assembly and microdispersal system. The ultracentrifuge can reach accelerations of up to 20,000 g (soils are generally run only up to 1,000 g), temperatures can be adjusted from -20 degrees to 150 degrees C, and constant flow rates can be reduced to 0.001 ml/h. Effluent from the sample is collected in a transparent, volumetrically-calibrated chamber at the bottom of the sample assembly.

Case Study: Uranium Transport in Hanford Soils

Figure 2 shows some transport results for uranium in a fine-grained Hanford soil under the unsaturated conditions existing in the field. The UFA was used to achieve field water content and conditions, i.e., 20 degrees C, a volumetric water content of 29%, and a hydraulic conductivity of 6.6 x 10^-8 cm/s using Hanford vadose zone water contaminated with uranium to 50 ppb. These steady-state conditions were achieved in 3 hours using the UFA. Similar experiments on the same soil using both traditional soil columns and negative-suction, or vacuum, columns took several months, and in one case over a year, to achieve steady-state under these conditions. However, results were consistent among all methods. Tritium experiments performed in the UFA gave R_f = 1 demonstrating that no preferential flow paths were being produced in the UFA and that all assumptions were correct. The breakthrough experiment for uranium itself took one month, e.g., the soil required almost 15 pore volumes of water pumping at 0.2 ml/hr to saturate the uranium sorption sites in the soil such that the contaminant could migrate unimpeded. The retardation factor was 7.6, a reasonably high value for soils of the Hanford Formation, especially under unsaturated conditions where there is a tendency to lower the effective retardation factor.( Lindenmeier, C. W., R. J. Serne, J. L. Conca, A. T. Owen, and M. I. Wood 1995. Technical Report PNL-10722, Pacific Northwest Labs, Richland, WA.) Chemical retardation can also be affected by the gas phase under unsaturated conditions, especially in this case, because the partial pressure of CO₂ adversely affects the solubility of uranium by forming relatively mobile carbonate complexes. This is why it is necessary to carry out column experiments under field conditions.

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