Challenges of Developing K_d Distributions from Literature Data - 21375

Partitioning of a contaminant between the solid phase and water phase in geological material via adsorption process can be modeled by using a contaminant specific partition coefficient K_d, which is a ratio between the concentration of contaminant absorbed on a solid phase and its concentration in the aqueous phase. It is known that K_d values are greatly dependent on aqueous and solid-phase chemistry. Consequently, measured K_d values can vary by several orders of magnitude for a contaminant. Probability distributions are used in modeling to capture the current state of knowledge regarding plausible values of K_d at the site. Ideally, these distributions would be developed using K_d data obtained experimentally from materials present at the site. However, such data are not always available, and applicable literature values need to be utilized. The main challenges of using literature data are their quality and applicability to a studied site. Due to the limited information regarding the scale, material, and method of data acquisition reported in the source, an extreme variation in plausible data for a contaminant is very common. Different strategies are used to overcome the challenges of using literature obtained K_d values. An application of one approach to dealing with these challenges in the distribution development process will be presented. First, data reliability weighting schemes are applied to account for source quality, method of data acquisition, data applicability, and site-specificity. In general, data obtained with experiments on materials sampled at the site receive the highest weight, while other data are down-weighted using predetermined criteria. Next, contaminants of interest in a risk-assessment model are divided into focus contaminants and other contaminants of interest. Focus contaminants are those that are likely to have the most significant impact on the model outcome and associated decisions regarding waste disposal. For each focus contaminant, a specific distribution by contaminant and geologic material (e.g., sand, soil) is developed by using available plausible K_d values that are collected by defining assumptions and criteria for site applicability. For other contaminants of interest, all available data are aggregated into groups by the magnitude of plausible K_d (e.g., low, medium, high). A generic distribution is then developed for each group using aggregated data across contaminants assigned to the group. The third step in distribution development is conceptual reasoning and the selection of robust statistical methods. K_d is experimentally determined and is prone to measurement error. For example, in batch experiments, a difference in concentration of the contaminant in the aqueous phase at the beginning and the end of the experiment is observed. This difference is very dependent on measurement error. Measured values are then used to calculate K_d. Column experiments have similar issues in a different setup. Calculation methods in the experimental determination of K_d are a cause of the relatively large error of determination in small or large K_d. Consequently, zero K_d cannot be reliably distinguished from small negative or small positive K_d values, while large K_d can be inflated. In order to develop appropriate distributions for plausible values of the parameter, these two related concepts lead to the use of censoring and the mixture of a discrete component of the distribution at 0 and a continuous gamma distribution for the positive part of the distribution. (authors)