Viscosity Prediction of Waxy Oils: Suspension of Fractal Aggregates (SoFA) Model

A new Viscosity model, called the Suspension of Fractal-Aggregates (or SoFA) model, is presented. It has been developed by considering waxy oil systems as suspensions of wax crystals that can interact and form fractal aggregates whose size is limited by the shear Stress tau. The Viscosity mu can be expressed as a function of the viscosity of the suspending liquid phase mu(L) and a function of the volume fraction of wax crystals phi. The constitutive law has the form mu = mu(L)(1 - A phi tau(-x)) [1 - (A phi tau(-x)/phi(M))(2)] if tau > tau(y) = (A phi/phi(M))(1/x) where phi(M) is the maximal packing fraction (phi(M) = 4/7) and A and X are parameters related to the structure and properties of the aggregates. If tau < tau(y), then mu = +infinity. Application of the 'SOFA constitutive law to,experimental flow curves has shown very good agreement matching the two model parameters A and X. Good results have also been obtained by using the Herschel-Bulkley, Li and Zhang, and Pedersen and Ronningsen models. The capability of the SoFA model to predict the viscosity of different systems at a given volume fraction of wax crystals phi has been successfully investigated. In this case, the n-paraffins distribution has been preserved. Only the physical properties Of the dispersing liquid phase have been changed. This first result gives us hope that such a model should enable the viscosity of live oil systems (presence of a gas phase) to be predicted However, to be definitively accepted for live oil application, comparison between SoFA model predictions and viscosity measurements in the presence of a gas phase under pressure will have to be carried out.