**4.1 Experimental procedure**

Tests were carried out for different sand slurries at flow conditions allowing easy mutual comparisons. During testing, sand mixtures of different degrees of grading were produced by combining the individual narrow-graded sands at various proportions of each sand in a resulting mixture (**Table 3**).

In test runs, the differential pressures were measured over the measuring sections along the pipe loop and the mean delivered concentration *C*vd was determined from the inverted U-tube or the other vertical-pipe section at various installed velocities *V*m. The local quantities—the concentration of solids in different vertical positions in the pipe cross-section and the solid's velocity at the bottom of the pipe—were measured as well.

## **4.2 Bimodal slurry flow**

The recent extensive broad-graded-slurry tests revealed that the flow of bimodal slurry composed of gravel and fine sand exhibited a considerably reduced friction loss compared to flow of gravel-slurry without the fine-sand addition [9]. It was hypothesized [10] that the major reason for the observed loss reduction was the reduction of mechanical friction between the sliding bed and the pipe wall and that this reduction was caused by a presence of a thin layer of fine-sand particles at the bottom of the pipe which at least partially separated the coarse sliding bed from the pipe wall. This hypothesis was indirectly supported by other results from the same experimental campaign, namely by those for bimodal slurry composed of medium-to-coarse sand and the same fine sand as in the former bimodal slurry. Flow of this bimodal slurry showed a negligible loss reduction by the fine sand. Since this flow did not contain a sliding bed, the result suggested that the friction reduction was effective only if the sliding bed was present. The actual presence of the fine separation layer could not be detected during the experiment due to the lack of flow visualization options.

A more detailed experiment was required to provide information about the internal structure of bimodal slurry flows. Such experiments had to include measurements of local concentrations and velocities of solids in the flow domain under investigation. The first runs from a series of such experiments were carried out for bimodal flows of ST1040 sand and STJ25 in our laboratory in 2020 [15]. Additional experiments followed with a different coarse-sand fraction (SS2030) and their results are discussed in this chapter.

#### *Settling Slurry Transport: Effects of Solids Grading and Pipe Inclination DOI: http://dx.doi.org/10.5772/intechopen.108436*

The bimodal 2S-slurry was composed of the coarse SS2030-sand and the fineto-medium sand STJ25 (**Table 3**). Tests were carried out for flow of the 2S-slurry at *C*vd ≈ 0.27 (0.19 of SS2030 and 0.08 of STJ25) and for flow of the corresponding one-species SS2030-slurry at *C*vd ≈ 0.19. Both flows were strongly stratified. The stratification was detected visually in the transparent section of the laboratory pipe and its degree was measured by a radiometric concentration meter in the measuring section of the laboratory pipe.

### *4.2.1 Visual observation*

The visualization confirmed the presence of the thin layer composed of the STJ25 sand at the bottom of the pipe. Furthermore, images of a camera directed to the bottom of the transparent pipe captured an interaction of coarse particles and fine particles at the pipe wall and clearly recognized that the finer STJ25 particles reduced the contact of the coarse SS2030 particles with the wall (**Figure 9**).

### *4.2.2 Solids distribution and local velocity of solids at pipe bottom*

Measured distributions of solids in the two comparable flows detected that the flow remained strongly stratified even when the finer sand fraction was added (**Figure 10**). Particles of the finer fraction increased the local concentration at all vertical positions in a pipe cross-section, including the positions in the sliding bed.

Developments in the longitudinal component of the instantaneous velocity of particles at the bottom of pipe were processed from high-speed-camera images over the period of a few seconds and then time-averaged. **Figure 11** compares time series of velocities of particles of the two fractions in the bimodal slurry at *V*m = 3.0 m/s. It shows that the finer STJ25-particles (red line) of the thin layer covering the pipe wall move slower than the coarser SS2030-particles at the bottom of the sliding bed. This suggests that the faster coarse particles slide over the slower finer particles of the thin separation layer.

**Figure 12** plots the development in the local velocity of coarse particles in the one-species SS2030-sand slurry corresponding with the bimodal slurry in **Figure 11**. **Figure 12** shows that the coarse particles at the bottom of the sliding bed are slower in this flow without the STJ25-additive than the same coarse particles in the bimodal slurry flow at the same flow velocity *V*m = 3.0 m/s and the same concentration of the coarse sand. This suggests that the presence of the STJ25-particles at the bottom of the pipe promotes the sliding of the coarse bed.

#### **Figure 9.**

*Camera images (magnified) of slurry at the bottom of the transparent pipe section (flow at Vm = 3.0 m/s). Left: Coarse slurry (SS2030). Right: Corresponding bimodal 2S-slurry (SS2030 + STJ25).*

#### **Figure 10.**

*Comparison of measured solids distributions in flow of coarse SS2030-slurry flow and of corresponding bimodal 2S-slurry at Vm* ≈ *3.0 m/s. Legend: Blue = SS2030-slurry, magenta = 2S-slurry.*

#### **Figure 11.**

*Measured time series of local velocity of particles of two fractions at pipe bottom for 2S-slurry flow at Vm = 3.0 m/s. Legend: Blue = coarse particles in 2S-slurry (horizontal line gives mean value); red = fine particles in 2S-slurry.* 

Time-averaged longitudinal velocities, *u*, plotted as horizontal lines in **Figures 11** and **12** were collected at two more velocities additional to *V*m = 3.0 m/s. The results are collected in **Figure 13** and give a more complete picture of the behavior of particles at the bottom of the pipe. **Figure 13** summarizes the velocities *u*c of coarse particles (in the bimodal flow and corresponding one-species flow) and *u*f of fine particles (in the bimodal flow). The plot shows that the coarse particles are faster than the fine particles at the bottom of the pipe (uc > uf) at all tested flow velocities *V*m in the bimodal 2S-slurry flow. Moreover, the coarse particles in the 2S-slurry are faster than the same coarse particles in the corresponding one-species coarse slurry at the same flow velocity *V*m.

#### *4.2.3 Friction loss*

The frictional gradients measured for flows of the bimodal 2S-slurry and of the corresponding coarse SS2030-slurry are compared in **Figure 14**. The bimodal slurry flow *Settling Slurry Transport: Effects of Solids Grading and Pipe Inclination DOI: http://dx.doi.org/10.5772/intechopen.108436*

**Figure 12.** *Measured time series of local velocity of coarse particles at pipe bottom for SS2030-sand slurry flow at Vm = 3.0 m/s.* 

exhibits lower friction losses than the corresponding coarse-slurry flow and thus the addition of the STJ25-sand caused the loss reduction as in the ST1040-based bimodal slurry tested previously. Note that the STJ25-sand particles have little effect on the friction loss if they are transported in one-species STJ25-slurry at a low concentration similar to the concentration at which they were added to the ST2030-sand slurry (**Figure 14**).

#### *4.2.4 Identification of friction-reduction mechanism*

The collected experimental information about the bimodal slurry flow and about flow of the corresponding coarse slurry without the finer-sand additive provides sufficient support for reasonable identification of the prevailing mechanism responsible for the friction reduction in the observed bimodal flow. As shown in **Figure 10**, both flows are strongly stratified. Therefore, the solid's contribution to their friction loss must be due primarily to mechanical friction between the sliding bed and the pipe wall. Hence, the observed friction loss reduction (**Figure 14**) must result from the reduction of this mechanical friction. The detected presence of a thin layer of STJ25 particles (**Figure 9**) between the pipe wall and the bottom of the sliding bed composed preferably of coarse particles (**Figure 10**) suggests that this layer is responsible for the loss reduction.

The information on the local velocities of particles at the bottom of the pipe helps to clarify the role of the thin layer. The observations suggest that its role is as follows:


#### **Figure 13.**

*Measured time-averaged local velocity (normalized by mean flow velocity) at pipe bottom for the flow of bimodal 2S-slurry and for flow corresponding SS2030-sand slurry. Legend: Magenta square = coarse particles in bimodal slurry (uc/Vm), magenta triangle = fine particles in bimodal slurry (uf/Vm), blue square - coarse particles in coarse slurry (uc/Vm).*

#### **Figure 14.**

*Measured dimensionless pressure gradient for bimodal 2S-slurry (SS2030 + STJ25 at Cvd* ≈ *0.19 + 0.08) and corresponding one-species slurries of coarse sand (SS2030 at Cvd* ≈ *0.19) and medium to fine sand (STJ25 at Cvd* ≈ *0.12). Legend: Blue square = SS2030-sand slurry; red triangle = STJ25-sand slurry; magenta diamond = bimodal 2S-slurry; black + = water.*

The coarse bed sliding easier and faster in the bimodal flow than the coarse bed of the same thickness (**Figure 10**) in the one-species flow, which also has a higher pressure drop, is a very strong indicator that there is a considerably smaller resisting force acting on the sliding bed from the pipe wall in the bimodal flow than in the coarse

flow. This reduction of the wall resisting force must be due to the presence of the thin layer at the wall and, therefore the layer is responsible for the friction reduction. In summary, the thin fine layer reduces contacts of coarse particles of the sliding bed with the pipe wall and so reduces resistance and energy consumption associated with mechanical friction between the sliding bed and the pipe wall.

#### **4.3 Broad-graded slurry flow**

Besides the bimodal 2S-slurry, two more broad graded slurries were tested. The 3S-slurry contains a mixture of three sands, SS2030, ST1040, and SP0612 (**Table 3**), and its *d*50 = 1.48 mm is very similar to *d*50 = 1.56 mm of the narrow-graded ST1040 sand. Measured friction losses are compared between the 3S-slurry flow and the ST1040-slurry flow of similar values of *C*vd in the left plot of **Figure 15**. The broader graded slurry obeys considerably less friction in the range of measured flow velocities.

The STJ25-sand is added to produce the 4S-slurry (**Table 3**) and to increase *C*vd from 0.25 to 0.31. As shown in the right plot of **Figure 15**, the friction loss reduces further by the STJ25-addition, exhibiting the same effect that STJ25 exhibited in the previously discussed bimodal slurry flows.
