Constitutive modelling and pipeline flow of thixotropic viscoplastic wastewater sludge

Due to the inherent rheological complexity of wastewater sludges, conventional sludge pipeline design based on simplified rheological models can result in inefficient sludge transportation systems. These inefficiencies are further exacerbated by a global need for the processing of more concentrated wastewater sludges that have a more pronounced non-Newtonian character, and hence require greater energy for transportation. However, the complex rheology of these materials (typically visco-elastic and thixotropic) requires sophisticated methods for constitutive modelling that are impractical to implement for complex materials such as sewerage sludges. We address this challenge by developing a novel viscoplastic thixotropic constitutive model that exploits the separation of timescales between the thixotropic and viscoelastic processes, leading to simpler and more robust experimental methods, parameter estimation and process simulation methods. This constitutive model combines a kinetic model for thixotropic degradation and agglomeration via a classical structural parameter (λ) approach coupled nonlinearly with a Herschel-Bulkley model to yield a thixotropic viscoplastic model of sludge rheology. Experimental data for thickened digested sludge between 3 and 4.9% solids were collected to validate the assumption for the separation of viscoelastic and thixotropic responses. The fitting procedure was found to be robust and efficient, and several rheological parameters were found to be invariant with solids concentration. Simplified energy calculations for a typical sludge pipeline showed that the pumping energy could be significantly under- or overestimated without considering thixotropy. These simple and robust constitutive models and fitting methods can accurately predict (and hence design and optimise) sludge behaviour over a wide range of wastewater processes.