(2c) Appropriateness of Mechanistic and Non-Mechanistic Models for Ultrafiltration of Mixed Waste

This study asks three questions: (1) How appropriate is the use of a basic filtration equation to the application of ultrafiltration of mixed waste? (2) Why are coefficients associated within the mechanistic model time invariant when the physical parameters within this coefficient are time varying? (3) How appropriate are non-parametric models for permeate rates (volumes)? To answer these questions, mechanistic and non-mechanistic approaches are taken for permeate rates and volumes associated with an ultrafiltration/mixed waste system in diafiltration mode. The mechanistic approach is based on a filtration equation which states that t/V vs. V is a linear relationship. The coefficients associated with this linear regression are composed of physical/chemical parameters of the system and based the mass balance equation associated with the membrane and associated developing cake layer. For several sets of data, a high correlation is shown that supports the assertion that t/V vs. V is a linear relationship. Some preliminary explanations for why coefficients associated with the mechanistic approach are time invariant are given. It is also shown that non-mechanistic approaches, i.e., the use of regression models to are not appropriate. Two models considered are Q(p) = a*ln(Cb)+b and Q(p)=Q0*exp(-kt). Regression models are inappropriate because the scale-up from a bench scale (pilot scale) study to full-scale for permeate rates (volumes) is not simply the ratio of the two membrane surface areas.