Eulerian-Eulerian Modeling of Non-Newtonian Slurries Flow in Horizontal Pipes

Abstract

Slurries transport through circular pipelines is present in many industries: oil, mineral, water and others. There are many variables involved in slurry flows, causing the flow behavior of these slurry systems to vary over a wide range, and therefore, different approaches have been used to describe their behavior in various flow regimes. At some typical applications, the rheology of the base fluid is itself non-Newtonian. Due to the wide range of variables and their variations, the experimental approach is necessarily limited by geometric and physical scale factors. For a non-Newtonian base fluid, only some particular cases that cover a limited range of conditions have been reported. For these reasons, numerical simulation constitutes an ideal technique for predicting the general flow behavior of these systems. Models in this area can be divided in two different classes: Eulerian-Eulerian and Lagrangian-Eulerian. Lagrangian-Eulerian models calculate the path and motion of each particle, while Eulerian-Eulerian models treat the particle phase as a continuum and average out motion on the scale of individual particles. This work focuses on the Eulerian-Eulerian approach for modeling the flow of a mixture of sand particles and a non-Newtonian fluid in a horizontal pipe. The steady-state rheological behavior of the base fluid was expressed by the three-parameter Sisko model. Homogeneous and heterogeneous flow regimes are considered. For the present study, the widely used “k-ε model” is employed to model turbulent viscosity. The k-ε turbulence model introduces two additional variables: the kinetic energy of the fluid turbulence, k, and the dissipation rate of this kinetic energy, ε. These two variables are solved throughout the fluid domain via two additional differential transport equations. The k-ε model is therefore commonly referred to as a “two-equation” turbulence model. The turbulent viscosity is then determined as a function of k and ε. Additionally, closure of solid-phase momentum equations requires a description for the solid-phase stress. Constitutive relations for the solid-phase stress, considering the inelastic nature of particle collisions based on kinetic theory concepts, have been used. Governing equations were solved numerically using the control volume-based finite element method. An unstructured non-uniform grid was chosen to cover the entire computational domain. A second-order scheme in space was used. Precise numerical solutions in a fully developed turbulent flow were found. Flow behavior for different sand concentrations was simulated. Results for the mean pressure gradients were compared with experimental data. The results turned out to be in compliance with those from the experimental data, for a sand concentration of less than 5%. Numerical simulations of non-Newtonian slurry flows provide a method that can relate properties of the fluid and solid component of the slurry, and does not entail the time and expenses needed for empirical studies. This also might provide a further sight to develop correlations between mean pressure gradients and slurry mean velocity.