Statistical comparison of non-Newtonian Laminar and Turbulant pipe flow pressure drop prediction models for sludges

Abstract

Most rheological and turbulent flow models for non-Newtonian fluids are nonlinear and deciding which one best represents the experimental evidence is not always obvious. Goodness-of-fit of non-linear models is often evaluated on the basis of root mean squared error (RMSE) or coefficient of determination (R2) which can be misleading and inappropriate for non-linear models. Pipe test data from the Flow Process and Rheology Centre, Cape Peninsula University of Technology were used to compare the power law, Bingham plastic, Herschel-Bulkley and Casson rheological models for 5% carboxymethyl cellulose (CMC) laminar data, and the Dodge and Metzner, Darby, Torrance, Wilson & Thomas, Slatter and El Emam models for bentonite and sludge turbulent flow data. The models were compared on the basis of RMSE, R2 and the Akaike Information Criterion (AIC). The RMSE and R2 criteria were useful in ranking models, but did not always distinguish between them, whilst the AIC approach clearly indicated the best model(s) in the candidate group. KEY WORDS: Akaike information criterion (AIC), model selection, non-Newtonian, RMSE, R2, turbulent flow