Verification and Application of Design Model for Settling Slurry Transport in Pipes

Abstract

The application of most empirical correlations for hydraulic gradient of settling slurry are generally limited to the experimental region in which four different flow patterns can be observed: stationary bed flow, saltation flow, heterogeneous flow, and pseudo-homogeneous flow. Therefore, the reliable design model independent on not only the flow regimes but also pipe diameter is imperative for pipeline engineers.By using the condition factor introduced by Sato et al., which represents the situation of solids movement in a pipe and calculated from the concentration profiles, an equation was derived for hydraulic gradient of settling slurry flow in horizontal circular pipes. With the slurry database, it was also assured that the equation was valid for practical pipeline design under the condition of settling slurry flow. Hence, the effect of pipe diameter and concentration on the Specific Energy Consumption and pipeline design procedure were discussed based on the analytical results.

Slurry Pipeline Design of Multi-sized Solids:Application of Innovated Models

“…For transporting fine and coarse solids in pipes, the coarse-fine model can be applied by a series of the following equations : (3) with: (5) where i si and i s = contributed hydraulic gradient of each particle size d i , and for all coarse solids calculated by the settling slurry model [3], while i v is hydraulic gradient of modified form of vehicle. If the portion of fine solids in slurry increases, the value of not only i but also V cd decrease, as shown in Figure 4.…”

The Multi-Sized Slurry Flows in Horizontal Pipes : Innovated Models and Verification

“…Assuming that each solid flow does not hinder the other, the hydraulic gradient of the slurry i is given as the sum of all the components, as follows : (10) where i w i sl and i s2 due to the coarse solids can be calculated by using the single size settling slurry model of Seitshiro et al, as follows [8] :…”

“…The hydraulic gradient of the slurry i is represented by : (12) where hydraulic gradients i v for modified vehicle and i s for all coarse solid portions, represented by Eq. (9), are estimated by using the Darcy-Weisbach equation and settling slurry model [8] respectively. Figure 10 shows the comparison of predicted hydraulic gradients i cal based on the Wasp method against the experimentals i exp of sand-bakelite mixed slurries in this study, Boothroyde et al and Shook et al As the concentration increases, the data tend to application of the Wasp method could be restricted to the range of lower concentrations of slurry, as pointed by Kaushal et al [7] Application of the single size model with average diameter d m to the wide range-size distribution data of Shook et al leads to large scatter, as shown in Figure 11.…”

“…They concluded that the Wasp method provided reasonable accurate results at limited low concentrations. The purpose of this paper is to discuss the limitations of application of other researchers' correlations and to develop innovated models, based on the single-size slurry model of Seitshiro et al [8] The analytical models depend on particle size distribution: (1) coarse-coarse model; for a slurry consisting of two fine particles in high concentration. The fine solids are defined as particles with sizes smaller than the critical diameter [9] in this study.…”