The U.S. Department of Energy's (DOE's) Hanford Site was developed during World War II to produce weapons-grade plutonium. This and other activities resulted in 60,000 metric tons waste stored in 177 underground storage tanks (UST). Some of these USTs have leaked into the subsurface. Because of this and other environmental concerns, DOE and Bechtel National, Inc. (BNI) are designing a Waste Treatment and Immobilization Plant (WTP) to treat the radioactive waste. A critical element of the WTP is an ultra-filtration process (UFP) that separates the radioactive slurry into high-level waste (HLW) and low-activity waste (LAW) forms. However, the productivity of the UFP in terms of HLW and LAW is in question and one approach to addressing production maximization is to understand the conditions to maximize permeate rates. This is predicated on understanding the relationship between axial velocity and pressure drop, which is the subject of this research. There are several approaches to modeling v versus Δp.

For example, researchers at Savannah River National Laboratory compared the Blasius model to experimental data collected from the Filtration Research Engineering Demonstration apparatus. They observed that the Blasius model under-predicted the data. Our approach is to use the Darcy-Weisbach equation, which includes a friction factor that has been determined using Prandtl's Mixing-Length Theory. The friction factor is a function of Reynold's number (Re) and a parametrically defined coefficient B. This B coefficient is possibly a function of several non-dimensional numbers. The results show that the appropriate model for B is a function of Cp (coefficient of pressure), which is shown to be equal to friction factor and length over inner diameter. The resultant model is compared with Blasius model and shows a higher goodness-of-fit. Also, the developed model for friction factors is dependent on physical scale and the effects of porosity are not significant. Through our understanding of this basic science, a better knowledge base will be formed to assess the productivity of the UFP, which helps the Pacific Northwest National Laboratory's goal to give research and development support to DOE and BNI.