Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 23
Issue 1
Civil Engineering
DOI:10.30825/5.ejpau.183.2020.23.1, EJPAU 23(1), #02.
Available Online: http://www.ejpau.media.pl/volume23/issue1/art-02.html


Victor Alexandrov, Arseny Kuzhelev, Anna Vatlina
Saint-Petersburg Mining University, Russia



The paper shows that in order to increase the efficiency of hydraulic transport systems in mining the transportation of slurries with a high concentration of solids in the slurry flow. Experimental studies have shown that slurry tailings of gold-containing ore with mass concentration of more than 55% are viscoplastic fluids. Experiments on a rotational viscometer allowed us to establish the main rheological characteristics of the studied slurries. Experimental studies of hydraulic transport performed on a laboratory setup, confirmed the results obtained on a rotational viscometer. Curved mixture streams are inclined straight lines that cut off on the axis of the head the sections, which determine the initial hydraulic slope corresponding to the shear stress yield on the rheological curves. According to the results of the experiments, a method has been developed for calculating the hydraulic transport of highly concentrated slurries of tailings of gold-bearing ore. Head loss values increase with increasing concentration. A sharp increase in head loss occurs in the concentration range from 60 to 65% and above

Key words: solid particles, concentration, shear stress, viscosity, head losses.


Hydrotransport systems at mining and processing plants in Russia are designed and built mainly in the 1960s and currently do not meet modern requirements for technical and economic efficiency and energy intensity of the process of transportation of ore processing tailings. The main reasons for this condition of hydrotransport systems of GOKs are low concentration of solids in the transported pulp flow large volumetric flows that require the use of high-capacity pumps; high intensity of metal for hydrotransport systems due to large pipe diameters and; significant energy costs for the return of recycled water in the processing. To improve the efficiency of hydrotransport systems, a complete modernization of the technological process of pumping tailings and the development of new design solutions is necessary. Such works are carried out according to the projects of reconstruction of hydraulic transport systems at mining and processing plants and according to the projects of the hydro-technical department of CJSC "Mekhanobr Engineering". The main idea of the projects for the reconstruction of hydotransport systems is transition to transportation of thickened tailings. The theoretical and experimental substantiation of design solutions is carried out by the Department of Mining Transport Machines of Saint-Petersburg Mining University [1, 2].

When designing hydrotransport systems for various slurries with high concentrations of solids, and in some cases for the paste state, it is necessary to consider:

The possibilities for thickening slurry of the tailings to high concentrations (more than 30% by volume of the slurry) depend primarily on the mineral composition of the ore being processed, the residual mineral composition of the tailings and the particle size distribution of the solid particles. In this case, we can assume that the structure of the flow is uniform, and the slurry is resistant to delamination, i.e. for a long time there is no visible separation of the pulp into liquid and solid phases. At high concentrations, the slurry of fine tailings becomes like pastes. The task of research in this work is to determine the optimal concentrations to ensure effective hydrotransport of thickened tailings using the example of the Verninskaya processing factory, taking into account the maximum possible concentration of the solid phase and the rheological properties of the pulp.


Graine size distribution. The granulometric composition of gold-bearing ore tailings from the Verninskoe deposit is represented by small particle size classes (Tab. 1). The integral curve of the particle size distribution is shown in Figure 1.

Table 1. Grain size distribution of the processing tailings of gold-bearing ore from the Verninskoye deposit
Size class  [di, mm] Content [Pi, %]
-0.15 + 0.1
-0.1 + 0.071
-0.071 + 0.045
-0.045 + 0.00

Fig. 1. Integral granularity curve

Taking into account hydrophobicity of the solid particles, they are well wetted with water and a shell is formed on the surface of the particles, and the particle itself turns into a dipole. Many small solid particles – dipoles in the considered volume of the slurry form a spatial structure (skeleton), at certain points of which there may be solid particles of larger fractions that do not have a significant effect on the overall structure, since the number of such particles is much smaller than the number of small particles – dipoles. Slurry of such solid particles for a long time does not separate into liquid and solid phase, i.e. they are stable. Sedimentation stability depends on the volumetric content of particles in the slurry. With an increase in the amount of solid phase (volume concentration), the stability of the slurry increases.

Density of solid material
Density of the solid material is 2700 kg/m3. The density of solid particles and their concentration determine the density of the slurry by the formula

ρh = cv (ρs – ρ0) + ρ0 (1)

where cv – volume concentration, ρs – density of solid, ρ0 – density of water.

The volume concentration can be expressed through water content in the slurry by the formula

cv = (ρs L + 1)–1 (2)

where L  – mass content of water in slurry.

From the ratio S:L is calculated mass concentration of the slurry:


where S – mass content of solid in slurry.

Productivity for solid tailings
The specified performance of tailings enrichment is:

Productivity in combination with density of a solid material and its concentration in the slurry stream determines the flow rate of the hydrotransport system, in accordance with the formula


From the formula it follows that with an increase in concentration or with a decrease in the proportion of water the volume flow of the slurry decreases. Figure 2 shows how  volume flow rate depends on  mass concentration cp.

Fig. 2. Pulp flow rate vs concentration of solid material

Preliminary calculations
For a preliminary assessment of the specific energy loss during hydraulic transportation of highly concentrated mixtures of tailings of gold-bearing ore, a calculation method developed for viscoplastic mixtures was used [3, 4]. A feature of the calculation method is the dependence of the parameters on the value of the Reynolds number. It is assumed that the pulp flow regime occurs in the region of hydraulically smooth pipes with the number Re = 3500–5000. With increasing concentration viscosity of the slurry increases and the flow regime approaches laminar. The calculated values are given in Table 2, where the values of mass – cp and volume – cv concentrations are indicated; S:L ratio; slurry density – ρh; volume flow of slurry – Qh; the calculated internal diameter of the pipe – Dpipe; average flow rate of slurry in the pipe  vm [m/s]; head loss (hydraulic slope) – ih  [m/km].

Table 2. Estimated results for hydrotransport thickened tailings of Verninskaya gold extraction plant
No cp
Reynolds number Re = 3500
1 0.536 0.3 1510 357.8 2.729 0.017 2.0 1/0.864
2 0.592 0.35 1592 306.8 1.504 0.048 4.0 1/0.687
3 0.648    0.4 1680 269.1 0.843 0.134 10 1/0.555
4 0.688 0.45 1765 238.6 0.479 0.368 21 1/0.453
5 0.73 0.5 1850 214.6 0.275 1.004 52 1/0.37
Reynolds number Re = 4000
6 0.592 0.35 1592 308.3 1.316 0.063 5 1/0.687
7 0.643 0.4 1680 267.8 0.738 0.174 11 1/0.555
8 0.688 0.45 1765 238.1 0.419 0.48 25 1/0.453
9 0.73 0.5 1850 215.2 0.241 1.311 64 1/0.37
Reynolds number Re = 4500
10 0.592 0.35 1592 301 2.122 0.079 5 1/0.687
11 0.643 0.4 1680 268.8 1.161 0.221 12 1/0.555
12 0.688 0.45 1765 239 0.656 0.608 29 1/0.453
13 0.73 0.5 1850 214.7 0.373 1.659 78 1/0.37
Reynolds number Re = 5000
14 0.592 0.35 1592 360 1.91 0.098 6 1/0.687
15 0.643 0.4 1680 306 1.051 0.273 14 1/0.555
16 0.688 0.45 1765 268.5 0.59 0.750 33 1/0.453
17 0.73 0.5 1850 237.8 0.335 2.048 97 1/0.37

Figure 3 shows graphical dependences of changes in the basic parameters of hydrotransport vs weight concentration of solid material in the range from 53,6 to 73%  that corresponds to the ratio

 and (30–50) % volume concentration. The specific pressure loss varies from 5 m/km to 64 m/km.

Fig. 3. Head loss (a), piping diameter, flow rate of mixture and average speed vs concentration of solid phase of the slurry

The data of Table 2 and the graphs in Figure 3 show that the flow parameters of the slurry are highly dependent on the solids concentration.  So 1.4 fold  increase in mass concentration causes 13 fold pressure loss increases while diameter of the pipe decreases 10 times average speed increases almost 60 times, and volumetric flow of the slurry decreases 1.6 times. Such ratios are also observed for other values of Reynolds number.

The relationship between head loss and shear stress is expressed by the following formula


where τw – shear stress on pipe wall:


The calculated shear stress values are shown in Table 3.

Table 3. Calculated values of shear stress on the pipe wall for various mass concentrations and Reynolds number
Mass concentration
Volume concentration
Solid to liquid ratio
Reynolds Number
Pulp density
Hydraulic slope
ih [m/m]
Shear stress
τw [Pa]
0.536 0.3 1/0.864 3500
1510 0.002 20.21
0.592 0.35 1/0.687 1592 0.004 23.4
0.643 0.4 1/0.555 1680 0.010 34.7
0.688 0.45 1/0.453 1765 0.021 43.5
0.73 0.5 1/0.37 1850 0.052 64.8
0.536 0.3 1/0.864 4000 1510 0.002 17.7
0.592 0.35 1/0.687 1592 0.005 25.7
0.643 0.4 1/0.555 1680 0.011 33.4
0.688 0.45 1/0.453 1765 0.025 45.3
0.73 0.5 1/0.37 1850 0.064 70
0.536 0.3 1/0.864 4500 1510 0.002 15.7
0.592 0.35 1/0.687 1592 0.005 22.7
0.643 0.4 1/0.555 1680 0.012 32.4
0.688 0.45 1/0.453 1765 0.029 46.8
0.73 0.5 1/0.37 1850 0.078 75.7
0.536 0.3 1/0.864 5000 1510 0.002 14.1
0.592 0.35 1/0.687 1592 0.006 24.6
0.643 0.4 1/0.555 1680 0.014 34.0
0.688 0.45 1/0.453 1765 0.033 47.8
0.73 0.5 1/0.37 1850 0.097 86.3

Figure 4a shows graphs of the change in shear stress on the pipe wall versus the Reynolds number. From the graphs it can be seen that in the mass concentration range from 0.536 to 0.665, the shear stress is directly proportional to the change in the Reynolds number. When the mass concentration is cp = 0.665 (S:L = 1:0.503; volume concentration is cv = 0.42), the shear stress for all the Raynolds numbers  is the same and equals 40 Pa. In this range of concentration changes, the values of shear stresses depend little on the Reynolds number. The point of intersection of the shear stress curves determines the effective concentration of the solid phase with equal values of the resistances on the wall of the pipeline. When the effective concentration is reached, the pressure loss during the pumping of the pulp will differ slightly from each other with a slight increase with a certain increase in the Reynolds number, Figure 4b.

Fig. 4. Dependence of shear stress (a) and pressure loss (b) on mass concentration of the slurry for various Reynolds numbers


To study the rheological characteristics of the hydromix tailings, experiments were performed on a rotational viscometer VT-350.  Obtained rheograms of shear stress (τw) versus shear rate, for mixtures with solid mass content of 60, 65, and 70%, are shown in Figure 5a.

Fig. 5. Rheological curves (a) and dynamic viscosity coefficient vs mass concentration of slurry (b)

The graphs show that maximum shear stresses occur in the slurry with a maximum concentration of cp = 70%. At the initial moment of the sensor rotation, maximum stresses were observed, which can be explained by the formation of a solid spatial structure in the volume of the slurry [5–8]. With an increase in the rotation frequency, the structural connections are destroyed, and the shear stresses decrease. At a frequency of rotation of 20 s–1, shear stresses take the smallest value (169.7 Pa), and with further increase in the speed of rotation a proportional increase in shear stresses occurs. The point of intersection of the continuation of the rheogram with the stress axis gives the values of the yield shear stress τ0. For slurry with a concentration of 70% the yield shear stress is approx. 129 Pa, 65%  concentration – τ0 = 68 Pa, at  60% – τ0 = 20 Pa. The tangent of the angle of inclination of the rheological curves to the abscissa axis determines the value of the dynamic coefficient of effective viscosity η. Thus for the mass concentration cp = 70% – η = 0.923 Pas; cp = 65% – η = 0.3258 Pas; cp = 60% – η = 0.2058 Pas. These values of viscosity make it possible to determine the nature of the change in viscosity as a function of concentration, Figure 5b. Curve in Figure 5b can be described by a power function of the form


where µ0 – dynamic coefficient of viscosity of pure (circulating) water [P·s]; k – experimental coefficient depending on the properties of the slurry (structural number n); cv – volume concentration of slurry.

For rheological curves of Figure 5a, it is possible to determine the functional dependence of the yield shear stress τ0, which is included in the Bingham-Shvedov formula. The graph is shown in Figure 6.

Fig. 6. Dependence of yield shear stress on mass concentration of slurry

Thus, all the parameters included in the Bingham equation were determined experimentally on a VT-350 viscometer. Using the obtained dependences, it is possible to calculate the magnitude of the pressure loss in a given range of changes in the concentration of the slurry. Taking into account the results of preliminary calculations and graphs shown in Figure 5 and 6, it is possible to determine the value of the maximum possible concentration of the solid phase in slurry. The results obtained must be compared with the experimental data on the pipes.


Experimental work to determine head loss during hydrotransport of tailings of the processing of gold-bearing ore was carried out on a laboratory pipe loop, the scheme and the general view of which are shown in Figure 7.

Fig. 7. Scheme of the experimental laboratory stand:
1 – tank; 2 – measuring tank; 3 – centrifugal pump; 4 – ball valve; 5 – piezometer; 6 – manometer; 7 – pipe D = 40 mm; 8 – pipe D = 50 mm

The experimental data, Table 4, show that head loss increases with increasing flow rate and with increasing mass concentration of the slurry. The maximum head loss of   0.524 mH2O/m was observed in experiments with concentration of 65%, and the smallest 55% concentration of slurry and head of  0.186 mH2O/m. Figure 8 shows graphical dependences of head loss on flow velocity, based on experimental data.

Fig. 8. Head loss vs average speed of slurry for different mass concentrations of slurry, from experimental data (i0 – yield hydraulic slope)

The flow curves are expressed by a linear function of flow velocity. Each slurry is characterised by a certain angle of inclination of the flow curve, indicating a change in the dynamic viscosity coefficient. The linear nature of the curves corresponds to the laminar flow regime. Intersections of flow curves with the coordinates indicates the values of initial hydraulic slopes – i0. The flow curves in Figure 8 can be represented by the following linear dependence

ih = i0 +kvm


where ih – head loss [mH2O/m]; i0 – initial (static) slope; k – coefficient of proportionality; vm – average velocity of slurry [m/s].

The calculated values of coefficient k and the corresponding Reynolds numbers are shown in Table 4.

Table 4. Calculated values of coefficient k and Reynolds number Re
Initial slope
(Fig. 8)


Reynolds number
0.65 0.524 0.33 0.194 0.3258 260
0.6 0.27 0.11 0.16 0.2058 390
0.55 0.195 0.06 0.135 0.144 520
Note: Values of dynamic viscosity coefficient h are taken from the graph in Figure 7, pipe diameter Dpipe = 0.05 m, average flow velocity is vm = 1 m/s.

Plots of coefficient k and initial hydraulic slope i0 as functions of mass concentration of slurry, obtained from Table 5, are shown in Figure 9.

Coefficient k varies linearly with the slurry concentration and can be calculated for all possible concentrations using the formula

k = 0.59·cp – 0.189


Fig. 9. Coefficient k and initial hydraulic slope i0 as dependent on mass concentration of the slurry

For known value of the k coefficient it is possible to calculate the value of pressure loss using the formula

ih = kvh + i0 = vh (0.59·cp – 0.189) + i0



The results of the experiments confirm that the slurry of tailings of gold-bearing ore from the Verninskaya processing factory at mass concentrations of 55% and above exhibit the properties of viscoplastic fluids described by the Bingham equation. The rheological curves constructed from the results of viscometric studies and shown in Figure 5 coincide in shape with the curves for head loss obtained from experiments in pipes (Fig. 7). The yield shear stress on the rheological curves corresponds to the values of the initial head loss on the curves of flow. The shear stress in the rheological curves correspond to the values of head loss in pipe. To determine the correspondence of the rheological characteristics to the experimental data on the pipes, it is sufficient to recalculate the values of shear stresses by the value of the head losses in the pipe.

For example:
mass concentration cp = 0.65; τw = τ0 + ηý.

Insert the data τ0 = 68 Pa (Fig. 5a), η = 0.3258  Pa·s (Fig. 5b);

The shear stress on the wall of the pipeline will be equal to τw = 68 + 0.3258·160 = 120 Pa. Head loss in pipe will be equal:


The actual value of the hydraulic slope measured during the experiments on the pipeline is iact = 0.524 mH2O/m.

Calculate the relative error of the results:


  1. Slurry of tailings of gold-bearing ore from the Verninskoye deposit with mass concentrations greater than 55% are viscoplastic fluids.
  2. Viscometric studies on a rotational viscometer allowed us to establish the main rheological characteristics of the slurries, i.e. – shear stress τw  and the dynamic viscosity coefficient η. Over the entire range of concentrations, from 55 to 65%, the flow of slurries is described by the Bingham rheological equation.
  3. The main rheological characteristics that determine the energy intensity of hydraulic transport are the yield shear stress τ0, the effective viscosity η, which are constant values for the slurry with a given concentration, and the shear rate ý, depending on the average flow velocity and diameter of the pipeline in the laminar flow region.
  4. Experimental studies of hydraulic transport, performed on a laboratory installation with a pipeline diameter of 50 mm, confirmed the results obtained on a rotational viscometer.
  5. Curved flows are inclined straight lines that cut off the segments on the axis of the head, which determine the initial hydraulic slope corresponding to the yield shear stress on the rheological curves.
  6. Recalculation of pressure characteristics to shear stresses showed that the average deviation of the calculated and actual results does not exceed 10%. This fact indirectly confirms the adequacy of the results obtained on a viscometer and on a laboratory hydro-transport setup.


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Received: 15.12.2019
Reviewed: 10.01.2020
Accepted: 29.01.2020

Victor Alexandrov
Saint-Petersburg Mining University, Russia
21 Linia 2
199106, Russia
email: Aleksandrov_VI@pers.spmi.ru

Arseny Kuzhelev
Saint-Petersburg Mining University, Russia
21 Linia 2
199106, Russia

Anna Vatlina
Saint-Petersburg Mining University, Russia
21 Linia 2
199106, Russia

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