Implications of Non-Bingham Rheology

One of the key challenges now facing the US Department of Energy (DOE) is the fate of radioactive waste remaining from World War II and the Cold War, which is stored underground in tanks some 75 feet in diameter and over 30 feet tall. Over time, the waste has segmented into multiple layers with sludges and slurries at the bottom with salt crust layers often at the top and liquid in between. DOE’s current official baseline plans call for remaining sludges and slurries to be removed from the tanks and converted into a stable glass waste form. Minimizing worker exposure to radiation drives DOE to use slurry processing techniques to suspend, mobilize, transport, mix, and process the waste. Therefore, a clear and quantitative understanding of Hanford waste rheology is essential for the success of the DOE mission. Historically much of the waste has been characterized using Eugene Bingham’s century old model that provides a straight line fit to higher shear rate data with the intercept suggesting a yield stress and the slope providing the consistency. Yet, Bingham fits overestimate the shear stress at a given shear rate for low to intermediate shear rates, exactly the range of shear rates typically encountered in pipe flow, where shear rates peak along the pipe wall and vanish in the center. This model produces a fictitious yield stress for some of the wastes that do not exhibit yield phenomena. While overestimating the yield stress may be prudent, safe, and conservative for some applications (e.g., pump sizing to ensure that pumps can handle yield stresses), overestimating the rheology may be inaccurate and non-conservative for other applications (e.g., eroding settled particle beds). Therefore, this paper evaluates the slurry rheology of Hanford and Savannah River wastes using a more modern rheological model that fits the full range of experimental data. Although a bias has been recognized and alternative models proposed, the magnitude of this bias and the implications for tank waste have only been qualitatively suggested. The purpose of this paper is to evaluate quantitatively implications of the poor quality of fit between a Bingham model for rheology and experimental data at modest shear rates. We first demonstrate the magnitude of the bias between the data and the Bingham extrapolation. We then evaluate quantitatively the velocity profile under laminar conditions. This analysis shows that the bias may be large (hundreds of percent or more) at modest shear rates and that modest shear rates dominate pipe velocity profiles.