Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry

Abstract

Mine transportation through hydraulic pipelines is increasingly used by various industries around the world. In Morocco, this has been implemented for the case of phosphate transportation. This allows to increase the production and reduce the transportation cost. Given the vital importance of phosphate in the global food security and regarding the huge amount of phosphate rock reserves in Morocco, it is detrimental to assess the reliability, to optimize and to increase its transportation in a safe manner. Usually hydraulic transportation of such fluids is fully quantified with a full characterization of its rheology related to its non-Newtonian behavior. The rheology allows to know the viscous and the elastic properties of a fluid exhibiting viscoelastic properties. In the case of water-phosphate slurry this behavior is not well-documented and classical constitutive laws for the rheology are of limited used, because of the high variability of different physico-chemical components of the slurry. The present work aims at quantifying the sensitivity of the water-phosphate slurry rheology to these components. In order to achieve this objective, a data-driven model based on polynomial chaos expansions (PCE) is developed and investigated. The choice of this class of models is motivated by the simplicity to conduct sensitivity analysis with the PCE and the limited amount of data available as the water-phosphate slurry pipeline is very new. In order to alleviate further the impact of the limitation given by the available data, we introduce the bagging technique which is an Ensemble based data-driven model using the PCE. Results presented in this study demonstrate that the bagging allows to reduce the validation error of the model by up to two orders of magnitude. Thus, it reduces considerably the variability on the estimation of hyperparameters in the model. Moreover, the sensitivity analysis shows that the variability on the elasticity coefficient is mainly due to the variability of the slurry density and the solid rate. Viscosity on the other side is not affected by the heterogeneity of the granulation distribution.