**Abstract**

In many industrial applications, settling slurries composed of coarse solid particles (typically sand or gravel) and Newtonian-carrying fluid (typically water) are transported in pipelines. Turbulent flow of such slurries consumes significantly more energy than flow of the carrying fluid alone. A contribution of transported solids to the energy loss is sensitive to solids grading and to the related distribution of solids in a pipe. Also related to the solid's distribution are changes in energy losses caused by an inclination of a pipe transporting settling slurry. We report on recent advances in the description and modeling of pipe flows of settling slurries with a special focus on the effects that the solids grading and the flow inclination have on flow friction. The description includes results of laboratory experiments and model predictions.

**Keywords:** hydraulic conveying, multispecies slurry, flow friction, solids distribution, pipe experiment

### **1. Introduction**

The size of a solid particle is one of the key parameters affecting the behavior of solid–liquid slurry flow in a pipe. The size determines the type of slurry and is responsible for prevailing mechanisms governing particle support and friction in slurry flow. A majority of predictive models for slurry flows consider just one characteristic size of transported particles and hence cannot take into account the profound effect a broad grading of solids can have on the slurry flow structure and energy loss due to friction.

For flows of settling slurries, it is well known that a considerable reduction of friction loss can be achieved if broadly graded solids are transported instead of uniformly graded solids of the same mass-median grain size [1–3]. Laboratory experiments on the effect of solids grading have been carried out primarily for bimodal slurries composed of two narrow-graded fractions of solids, each of different particle size [4–7].

Recent extensive experiments with various combinations of up to four different fractions of solids of the same density (each representing one type of settling slurry: fine, pseudo-homogeneous, heterogeneous, and stratified, respectively) [8] demonstrated a considerable effect that finer fractions added to coarse stratified flow have on the friction loss and enabled its quantification. An analysis of bimodal slurries

tested in these experiments and composed of the coarse stratified fraction and one additional finer fraction (either the fine or pseudo-homogeneous or heterogeneous) showed that the effect of each of the added fractions on the friction loss is different and thus caused by a different mechanism [ 9 ]. Other laboratory experiments showed that the broad grading also affects the solids distribution in settling slurry flows [ 6 , 7 ].

 Our experimental investigation, combining observations of flow friction and solids distribution in settling slurry flows of various solids compositions, has aimed to identify mechanisms responsible for the effects that the particle size and the particle size distribution have on friction losses in horizontal and inclined flows. The first results have been published for a limited number of tested solids and flow conditions recently [ 10 – 15 ]. New results are discussed below.
