Discussion of PNL Scaleup Method

The test data show that the conditions required to completely clean the coupon of silicone oil are a pressure of 105 bar at a temperature of 45°C with an impeller speed of 1000 rpm. To scale up this process for use with actual parts contaminated with a similar material, we must first decide which criteria to include for achieving similitude. Since temperature and pressure are intrinsic values that do not rely on any other aspect of the prototype design, except that it must be able to hold the desired pressure at the desired temperature, the mechanisms governing mass transfer and agitation become paramount. 

The movement of a contaminant near the surface of a part to the bulk fluid is governed by mass transport mechanisms. The molar flux of a species A from a surface may be expressed in terms of a composition driving force and a mass transfer coefficient  

Mass transfer coefficients are typically correlated using a dimensionless quantity known as the Nusselt number for mass transfer shown below  

For flow in a pipe, the pipe diameter is conventionally used as the characteristic length. For flow around a submerged sphere, the sphere diameter is used as the characteristic length. For flow past a 

In general, the Nusselt number is a function of the Reynolds number (Re = vxp/p), the Schmidt number (Sc = i/pD ), system geometry, and the magnitude of the mass flux. For the case of smaller mass-transfer rates, the Nusselt number depends less on the magnitude of mass flux. For small mass-transfer rates, heat and mass transfer become analogous in this case similar forms of heat and mass transfer correlations can be used to describe the same geometry  

Nujf = Nusselt number for mass transfer, dimensionless 

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