High Concentration, Coarse Particle, Hydraulic Conveying

Abstract

Conventional coarse particle hydraulic conveying is performed under turbulent flow conditions, usually at concentrations of less than 40% v/v. The last three or four decades have seen the development of much higher concentration conveying, with the successful transport of suspensions of 70% v/v or more. These suspensions can be conveyed at very low velocities and generally exhibit very benign characteristics, having the capability of being stopped and restarted at will. There are generally two methods of pumping coarse materials safely at low velocities. The first method, using a Newtonian such as water, can be applied when the particle size distribution is sufficiently broad to minimize percolation and the concentration sufficiently high to prevent particle restructuring during transport. A second method uses a non-Newtonian, visco-plastic carrier fluid, normally fine particle slurry, to convey the coarser particles. This second method removes the constraints of the first method, allowing a greater range of coarse solid distributions and concentrations to be pumped. In both cases, the conveying characteristics appear similar to laminar flow. Both methods are described and analyzed in this chapter.

1. Introduction

Except for the transport of pastes and non-Newtonian slurries, most hydraulic transport applications operate under turbulent conditions at low to moderate volumetric concentrations. This contrasts with pneumatic transport systems which operate in both dilute, or lean, phase conveying and dense phase conveying. Dilute phase is analogous to this form of hydraulic conveying, while dense phase conveys solids at much higher solids’ concentrations and at lower velocities. Over the last three or four decades, advances have been made in the development of higher concentration hydraulic transport systems, which share many characteristics in common with dense phase pneumatic systems.

Conventional hydraulic transport systems are turbulent, relying on the action of turbulent eddies to suspend and convey the solids in the pipe. At high velocities, the solids’ suspension is almost uniform across the pipe, while at lower velocities, a pronounced concentration profile appears, forming sliding and even stationary beds of solids on the bottom of the pipe. Such flows are unstable and solids’ transport will stop when the mean velocity falls below a minimum conveying velocity, and may even block the pipe. To minimize this risk of blockage and assist in restarting, a rule of thumb is used whereby the in-line solids’ concentration, Cv_i, is generally limited to less than 40% v/v. The minimum conveying velocity is a function of the solids’ concentration, size and density, and can typically range from 1 to 2 m/s for fine particles (d < 1 mm say) to 7–10 m/s for coarse particles (d > 5 mm say).

Despite these unstable characteristics, such conveying has many advantages in the main areas where it is practiced, namely inter-process transfer, dredging, tailings disposal and long distant transport of ore or concentrates. It is simple to operate, requiring only that those solids are mixed with water in a suitably agitated vessel of some form, and pumped, normally using centrifugal pumps, through the pipeline to their destination. The low concentration also affords easy separation of the solids from the conveying fluid.

By contrast, outside of the food and some process industries, high concentration conveying is rarely seen, concrete pumping being the most obvious exception. However, high concentration systems have been developed and are finding increasing use in tailings disposal, hoisting and other niche applications. Their attractiveness lies in their benign operation, as they generally do not require a minimum conveying velocity, so lines can be stopped and restarted at will. Their low velocity, typically of order 1–2 m/s, several meters per second lower than their coarse particle low concentration counterparts, results in low particle attrition and pipe wear. This mode of conveying also allows very coarse particles to be conveyed at low particle pipe diameter ratios, e.g., D/d ≤ 5. The high concentration, $40<\mathit{Cv}\le 75\%$ v/v, also produces low specific energy consumption (SEC), producing low operating costs (OPEX) and low greenhouse gas emissions. These advantages, however, are offset against a more complex operating system and the need for more specialized equipment (CAPEX).

Two forms of high concentration conveying have been developed, one using Newtonian fluids, like water, as the carrier fluid to convey the solids, and a second using non-Newtonian carrier fluids. Although sharing many characteristics, these methods will be described separately starting with the Newtonian system.

2. Newtonian high concentration conveying

2.1 Concentration considerations

While weight concentration, Cw w/w, or worse weight of solids per volume of liquid, Cwv w/v, are common in industry, it is the volumetric concentration, Cv v/v, that characterizes and controls the way a suspension of solids behaves. At high concentrations, another more useful way of describing the solids’ concentration is the ratio of the volumetric concentration to the maximum packing concentration of the solids, or more usually the maximum dilated or loose poured concentration, i.e., Cv/Cb known as the reduced concentration. The term Cb is used here to denote this packing concentration, as this value corresponds to the in-situ concentration of a settled or sliding bed of solids within the pipe. For non-Newtonian systems, described in §3, the bed concentration will be lower than for Newtonian systems, and will be described in greater detail there. This value may be considered to indicate the pipelines obscuration, or particle’s mobility.

Cb is a function of the particle’s size distribution (PSD) and shape distribution (SSD), from which this value can be calculated (for example [1, 2]), or measured using a procedure outlined by Leuenberger [3], as follows. A tank of initially dry solids is continuously mixed with a pitch-bladed agitator, and the power drawn by the agitator monitored while water is progressively added. An example of such a test is shown in Figure 1.

Figure 1.

(a) Broad PSD of typical run of mine (ROM) coal, (b) experimental value for two different agitator speeds and calculated (dashed line) determination of Cb for the same ROM.

The typical response to the addition of water (Figure 1b) is to change the solids from a purely granular flow in air, to one where an increasing number of water bridges are formed. Shearing these as well as the solids requires increasingly more energy. Once all the interstices are filled with water, further addition of water simply separates the particles, reducing the mixer energy requirements. Thus, the value of 1- Cv_water corresponding to the peaks in the characteristic curves approximates Cb.

The calculated value of Cb, based on the coal’s PSD and SSD, is approximately 89%, whereas the empirical value is around 86%. The discrepancy, although small, is because the empirical value is for a sheared, and hence a dilated bed. It is recommended that the empirical value is used, or that calculated values should be reduced by a couple of percentage points.

2.2 Conveying characteristics

As mentioned in the introduction, both dilute and high concentration conveying is commonplace in pneumatic conveying systems, and the operational or transport characteristics are displayed in what is known as a diagram of state (Figure 2).

Figure 2.

Diagram of state for coarse particle pneumatic conveying.

At moderate to high velocities, the transport characteristics exhibit the familiar hook curves of conventional hydraulic conveying systems, moving from a fully suspended state at high velocities, to sliding beds as the velocity is decreased. After going through a minimum, the pressure gradient rises due to partial obscuration of the pipe and increased particle wall contact. For hydraulic systems, which normally use centrifugal pumps, this is an unstable region, but for pneumatic systems, which use a variety of different feeding systems, e.g., blow vessels, transport can still be obtained down to very low velocities. At these low velocities, the line is filled with solids that move along as a continuous plug, although this plug is often deliberately broken into smaller plugs to reduce the pressure requirements. At intermediary velocities, however, the flow is unstable, exhibiting dune flow that can block the pipe.

Wilson et al. [4] examined the behavior of dense phase hydraulic hoisting, subsequently publishing an analysis of the frictional component of such plug flow [5], and such techniques were employed in the Hansa underground mine to hoist -60 mm coal, 850 m to the surface [6]. To the author’s knowledge, though, it was not until the invention of a feeding system called a Rotary Ram Slurry Pump (RRSP), described in §2.7, that dense phase horizontal coarse particle hydraulic conveying was considered at an industrial scale.

The RRSP enabled very high concentrations of coarse particles to be loaded into a pipe using a valving system that opened to the full bore of the conveying pipe. These particles could be conveyed at very low velocities with little, if any, inter-particle movement. This feature was ideal for friable materials such as coal. Transport characteristics for ROM coal conveyed in a 300 mm pipe using this technique are shown in Figure 3.

Figure 3.

Typical high concentration, coarse particle, transport characteristics. Computed curves of constant delivered concentrations and partial deposition locus using a two-layer model. The bed depth Y_bed is also shown.

The transport characteristics do not exhibit the typical hooked curves of lower density conveying, although transport below the lowest velocities shown were problematic. Suspensions with concentrations below 65% were also unstable for this particular material. Readings from an isolated electrode probe (see e.g. [7]), inserted into the top of the pipe, registered periodic high activity at these lower concentrations, indicating possible dune formation. A two-layer model, at concentrations close to plug flow, was used to model this flow with satisfactory agreement as shown. However, the adoption of a normal two-layer model is found to substantially overpredict the transport pressure gradients shown, and modification to such a model is needed before the agreement shown here is obtained.

2.3 Two-layer modeling modifications for coarse particles

Only a simple two-layer model (e.g. [8]) will be used in this section for illustrative purposes, and the reader is referred to the chapter on Pipeline Modeling for a more complete description and a more nuanced approach. The early layered models were developed to model the behavior of small sand particle slurries, which become fluidized during transport. This is evident by observing slurry issuing from holes in the upper invert of the conveying pipe, where the slurry behaves as a fluidized jet [9]. Such behavior is not observed in coarse particle flow. This difference has ramifications for the modeling of the resisting force of the bed in a two-layer model. Consider the schematic of the pipe cross section shown in Figure 4a.

Figure 4.

(a) Schematic of pipe cross section giving the normal force distribution for fine and coarse particles, (b) wear pattern in a 300 mm pipe used for conveying -32 mm solids, showing unworn original oxide coating in pipe upper invert.

If the solids are fine and fluidized, the bed presents a hydrostatic pressure at the pipe wall (Figure 4a, left hand side), which is normal to the pipe wall. If the density of the fluid and solids are ρ_f and ρ_s, respectively, then the normal force of the bed on the pipe wall is given by

$$N=2\mathit{Cb}\left({\rho }_s-{\rho }_f\right){\mathit{gR}}^2{\int }_0^{\beta }cos\left(\beta \right)-cos\left(\theta \right)\mathit{d\theta }$$E1

Where β is the half bed angle shown in Figure 4a and which on integrating and rearranging becomes

$$N=2\mathit{Cb}\left({\rho }_s-{\rho }_f\right)g\frac{D^2}{4}\left(sin\left(\beta \right)-\beta cos\left(\beta \right)\right)$$E2

Conversely, for unfluidized coarse particles the normal force is simply

$$N=\mathit{Cb}\left({\rho }_s-{\rho }_f\right)g\left(\frac{\pi D^2}{4}\right)\left(1-A\right)$$E3

where A is the fractional cross-sectional area above the bed and (1-A) is the area of the bed $\left(1-A\right)=\left(\beta -sin\left(\beta \right)cos\left(\beta \right)\right)/\pi =\mathit{Cv}/\mathit{Cb}$.

The difference between Eqs. (2) and (3) is then a multiplier which accounts for the effect on the resisting force of particle fluidization. Thus, combining Eq. (2), Eq. (3), the bed fractional area and a degree of fluidization 0 < f < 1, where a value of zero = the unfluidized state, 1 = the fully fluidized state, this multiplier can be written as

$$F=1+f\left[2\frac{sin\left(\beta \right)-\beta cos\left(\beta \right)}{\beta -sin\left(\beta \right)cos\left(\beta \right)}-1\right]$$E4

and used to describe the bed’s normal force for an arbitrarily fluidized bed by

$$N=\mathit{Cb}\left({\rho }_s-{\rho }_f\right)g\left(\frac{\pi D^2}{4}\right)\left(1-A\right)F$$E5

2.4 Comparison with conventional conveying

Data reported by the Saskatchewan Research Council (SRC) for coarse coal in water [10] show typical results in a similarly sized pipe for -50 mm solids, d₅₀ = 3 mm, Cv = 0.457 v/v, D = 234 mm, to be V = 2.5 m/s, dP/dx = 0.64 kPa/m. The conveying velocity is higher than that shown in Figure 3, and this, combined with the lower concentration means that particle attrition would be considerable. The pressure gradient, however, is comparable to that of the 70% curve in Figure 3. A comparison of the operating costs can be achieved by comparing the SEC given by

$$\mathit{SEC}=\frac{\text{suspension pumping power}}{\text{solids mass flow}\mathrm{x}\text{distance}}=\frac{\raisebox{1ex}{$\mathit{dp}$}\!\left/ \!\raisebox{-1ex}{$\mathit{dx}$}\right.}{3.6\mathit{Cv}\raisebox{1ex}{${\rho }_s$}\!\left/ \!\raisebox{-1ex}{${\rho }_f$}\right.}\raisebox{1ex}{$\text{kWhr}$}\!\left/ \!\raisebox{-1ex}{$\left(\text{tonne}\mathrm{km}\right)$}\right.$$E6

where the pressure gradient, dp/dx, is in kPa/m.

Comparing the SRC data with the higher pressure gradient 75% v/v data, the SEC for the conventionally conveyed coal is 0.27 kWhr/(tonne km), compared with 0.23 kWhr/(tonne km) for the high concentration conveying. Furthermore, the high concentration system consumes 45% less water. A more detailed comparison of high concentration and non-Newtonian systems, described in §3, with conventional conveying is given in [11].

2.5 Restart capabilities and practical considerations

2.5.1 Restart

As mentioned above, transport at lower concentrations proved problematic through dune formation partially blocking the pipe, resulting in unsteady flow. Experience gained with the RRSP suggested that an operational concentration range should be limited to 0.75 < Cv/Cb < 0.9, and that the materials required a broad size distribution such that Cb > 0.75 to avoid excessive bed percolation of the low viscosity water carrier.

When operating within these constraints, restart of fully loaded pipelines several kilometers long proved to be immediate once the pumps were activated. The explanation for this is not entirely clear but is expected to relate to the low deposition velocities. The deposition locus for the material in Figure 5 expressed as a function of Cv/Cb is shown here (Figure 6).

Figure 5.

Normal force fluidization modifier for f = 0, unfluidized coarse particles, f = 0.5, partially fluidized intermediary particles, f = 1 for fully fluidized fine particles.

Figure 6.

Deposition locus as a function of Cv/Cb for the data shown in Figure 3. The concentration limits for successful operation are shown shaded.

At the operational limits for this material the corresponding deposition velocities are approximately 0.6 and 0.2 m/s. Such suspensions started with ease, and it is expected that once the pumps were started, increasing the flow to the normal conveying velocity of a 1 m/s was sufficiently rapid so that reorganization of any particles above the bed to form a plugging dune did not occur. This is despite the high velocity fluid flowing over the beds, which occupy 75 to 90% of the pipes CSA.

2.5.2 Practical considerations

Production of such suspensions is comparatively easy as the mobility of these suspensions is very high, requiring only gentle agitation in suitable mixing tanks to ensure homogenization. More difficult is maintaining the high concentrations within the required limits, requiring conveyors etc. to be sheltered from rain, and sufficient surge capacity to be installed for constant operation. This last point is less of a problem, as the ability to reduce the transport velocity to very low values or stopping, provides a very large turn down ratio. Maintaining the correct feed to the pump also requires some care, as fluid can be preferentially drawn from the tank diluting the flow into the pump’s inlet ducting, producing unstable operation, details of which are described in [12].

2.6 Diagram of state for hydraulic conveying systems

A diagram of state, similar to Figure 2, can now be drawn for hydraulic systems, to include high concentration transport, and is shown in Figure 7.

Figure 7.

Diagram of state for water based coarse particle hydraulic conveying.

The similarities between Figures 2 and 7 are strong, showing very similar characteristics for dilute or conventional hydraulic conveying, as well as low velocity high concentration flow. In this case, though, rather than the unstable region being simply a function of conveying velocity, it is now a function of solids’ concentration being problematic at the intermediary concentrations.

Before leaving this section on Newtonian systems a brief description of the RRSP will be given, although it is noted that other solids feeders can also be successfully employed, e.g. the Kamyr feeder or similar, and various lock hopper systems (e.g. [13]).

2.7 Rotary ram slurry pump

The RRSP was invented by Bede Boyle [14, 15] and further developed by the ASEA Mineral Slurry Transport group [16], who built a 300 mm pipe diameter unit capable of transporting 300 dtph of coarse coal. A schematic illustrating the basic operating principles of this device is shown in Figure 8.

Figure 8.

(a) Partially sectioned schematic of a rotary ram slurry pump, (b) schematic of discharge end of rotating barrel showing the filling and discharging process. Kidney valve locations shown dashed.

The RRSP comprises a barrel, like that in a revolver, containing a multiple number of diametrically opposed paired cylinders and pistons, that rotates on hydro-static bearings inside a casing. The configuration of a four-piston cylinder assembly is shown in Figure 8a. Two stationary valve plates each containing a full-bore inlet and full-bore outlet kidney valves are located at either end of the barrel, as shown. Manifolds containing inlet and outlet ducts are attached outboard of these valve plates. The cylinders comprise two bores of different diameters, with the smaller bore at the suspension discharge end of the RRSP. The pistons that run in these cylinders similarly have two diameters to suit the bores in the cylinders. The barrel is rotated by a hydraulic motor, mounted at the water end of the RRSP (right in this Figure), such that the cylinder openings pass the kidney shaped openings in the valve plates, allowing material to periodically enter or exit the cylinders. The upper duct, at the water end, is connected to the output of a multi-stage, high pressure, water pump, and supplies the motive force to drive the suspension. Water is returned via the lower duct to a sump. At the discharge end of the RRSP (left in this figure) the lower duct is connected to a stirred tank containing the suspension to be conveyed, and the upper duct is connected to a matched diameter conveying pipeline. The operation of the RRSP is as follows. While the upper cylinder is exposed through the kidney valve to the high-pressure water supply, the piston is driven forward, discharging the suspension that is in the smaller cylinder into the pipeline. Water contained in the annular volume between the larger upper cylinder and smaller upper piston passes through the transfer port indicated to drive the lower piston backwards. This action induces suspension from the stirred tank through the kidney valve and into the lower smaller cylinder. Since the barrel is continuously rotating, these cylinders move to their horizontal locations, to be replaced by the next pair, indicated in Figure 8b, and ultimately to their near vertical location, where the process is repeated. The valving is designed so that contribution from the total of each cylinder pair produces essentially constant continuous flow.

The RRSP’s design enables very high concentrations of large particles to be transported, by virtue of the use of the high-pressure centrifugal pumps, rather than by driving the pistons through mechanical means. As the cylinders rotate and the upper suspension cylinder starts to be exposed through the kidney valves to the pipeline, large particles in the cylinder will not be able to pass through the initially small valve opening. The suspension will be compressed, and the piston stopped. As the driving force is supplied by a centrifugal pump, this simply means that the pump’s pressure will rise to its shut-off head. The valve opening continues to increase until it is large enough for the trapped particles to pass, and transport continues. This, combined with the full bore opening of the valves, enables very large particles to be conveyed and values of D/d < 5 were conveyed as normal practice, compared to the normal upper limit of D/d > 10 imposed in conventional conveying.

3. Non-Newtonian high concentration conveying

3.1 A brief history

In the early 70’s, tests examining the effect of hydraulic conveying on high concentration coarse coal suspensions [17] showed that as the coal degraded, the transport characteristics changed from the normal turbulent hook curves, to lines that were characteristic of laminar flow, and that the solids could be conveyed at much lower velocities.

These results instigated work into what became known as Stab Flow, whereby research was conducted into the “laminar” behavior of these suspensions, with various researchers (e.g. [18]) reporting linear relationships of the familiar form ${\lambda }_m=64/{\mathit{Re}}_m$, where λ_m and Re_m are the mixture friction factor and mixture pipe Reynolds number. Vertical concentration profiles taken across the horizontal pipes, using traveling densitometers, showed the variation across the pipe to be minimal (e.g. [19]). Such results supported the notion of homogenous behavior for these suspensions. The influence of pH in the data of Figure 9b demonstrated that rheology of the underlying carrier slurry, or carrier fluid, was important, but it seemed that the coarse solids, despite their size, could somehow be combined with the properties of the carrier fluid and be modeled using homogeneous non-Newtonian methods.

Figure 9.

(a) Typical conventional conveying characteristic for −12.5 mm coal, (b) “laminar” characteristics for degraded −12.5 mm coal, after Elliot & Glidden [17].

Figure 10a demonstrates how convincing such an approach can be. Here all suspensions are seen to behave like homogeneous fluids. The originally presented curves were calculated using non-Newtonian laminar relationships and semi-empirical predictions of turbulent flow, using a suspension pseudo-rheology, based on the underlying carrier fluid rheology and coarse particle concentrations, i.e., τ_ym = f(τ_yc, Cv) etc., where subscripts c and m denote carrier fluid and suspension respectively.

Figure 10.

Coarse mine waste suspensions (after Duckworth et al. [20]). (a) Curves based homogeneous non-Newtonian suspensions with rheology a function of the carrier fluid and coarse concentration, (b) non-Newtonian two-layer model predictions.

Several groups adopted this pseudo-rheological approach to predict full size data and scale up of test data, but this was found to only be successful for relatively minor increases in scale, and, as demonstrated by the dependence on pH, required that the underlying carrier fluid’s rheology would stay constant.

Anecdotal evidence, later confirmed by tomographic studies (described in the chapter on tomography in this text) and flow visualization studies, showed that rather than being homogeneous, such flows were stratified. This allowed mechanistic two-layer models, based on the carrier fluid and particle properties, to be used to predict and scale up the data. Such predictions are shown in Figure 10b. Flows such as these are now generally analyzed using layered models, which produce predictions of transport pressure gradients typically within less than 10%.

During this period, the introduction of high rate and deep cone thickeners allowed a new form of tailings disposal to be developed [21], whereby rather than conveying low concentration solids to settle in conventional walled TSFs, high concentration non-Newtonian suspensions were pumped out onto a flat TSF. The discharged suspensions formed cones of solids that were stabilized by the yield stresses in the underlying carrier fluid. Such TSFs had a smaller footprint than their conventional counterparts, did not incur the expense of large bounding walls, were inherently safe, not being susceptible to catastrophic wall breaches, and could be rehabilitated earlier.

Thus, there was a perceived need to adopt this technology to (i) transport coarse materials at low velocities, and (ii) to dispose of large quantities of waste material in a more economic and environmentally safe manner.

3.2 Stratification process

Stratification when the flow is turbulent is performed through a similar process for non-Newtonian based suspensions as it is for Newtonian suspensions. The higher viscosity and differing viscosity distribution means that moderately sized solids are more readily suspended and adopt a more uniform concentration distribution than their Newtonian based counterparts [22].

In laminar flow, there are no turbulent suspending eddies, but if the carrier fluid is a visco-plastic, with a substantial yield stress, this yield stress will be able to support the particle if it exceeds a critical value τ_yc, i.e.

$${\tau }_{\mathit{yc}}=\mathit{kgd}\left({\rho }_s-{\rho }_f\right)k\approx 0.1\text{for irregular particles}$$E7

However, in sheared visco-plastic flows, the fluid surrounding the suspended solids is subjected to a shear rate equal to the vector total of all applied shear rates, i.e., the local velocity profile, that due to the particles’ settling motion and that due to any rotation of the particle. This shear rate is finite, and since visco-plastic flows are very shear thinning, this means that the viscosity of the fluid, local to the particle, will have a high, but finite viscosity, and so the particle will be able to settle through it. It has been shown [22, 23, 24] that at particle Reynold’s numbers, typical of settling in non-Newtonian pipeline flows, the settling velocity of the particle can be calculated using Stoke’s relationship, providing this local viscosity is used.

In visco-plastic pipeline flow, there exists a central core that is unsheared, and thus if the carrier fluid’s yield stress exceeds τ_yc, any particle that is within this plug will not settle. This argument was used to support the apparent homogenous behavior of Stab Flow, and furthermore it was suggested that Magnus forces, in the sheared annulus, would transfer particles from there into the unsheared plug, such that the flow became a form of lubricated capsule flow, affording very low transport pressure gradients.

Consider the coarse suspension pipeline flow, shown in Figure 11, where the carrier fluid has a yield stress greater than that required for static support, i.e., τ_y > τ_yc.,

Figure 11.

(a) Initial coarse particle suspension flow as it enters the pipeline, (b) bed development further along the pipe, (c) averaged chord and vertical Centre line concentration profiles, obtained using electrical resistance tomography (ERT) [24].

Suspensions entering the pipe from a well-mixed tank at volumetric concentration Cv_i will be uniformly distributed across the pipe (Figure 11a), and once the wall shear stress exceeds the yield stress an annular sheared region (r > r_p) will be formed, as shown. Particles within the unsheared core will be statically supported, but those in the annular region will be subjected to shear, and so will settle. Further down the pipe (Figure 11b), the particles from the annular region have settled to form a bed (stationary or sliding depending upon the conditions) at concentration C_vb. The presence of the bed distorts the flow such that the dynamic center of the flow moves from the pipe axis, to midway between the top of the bed and the upper pipe wall. This distorts the conical stress distribution of the homogenous case, and while it remains linear on the vertical plane of symmetry, it becomes distorted elsewhere. The unsheared plug now adopts an essentially elliptic form, centered on the dynamic center, of major and minor diameters, approximated by

$$p=\frac{\mathit{\zeta D}}{2};q=\frac{\zeta \left(D-y_b\right)}{2}$$E8

where $\zeta ={\tau }_y/{\tau }_w$ and y_b = the depth of the bed.

The unsheared plug’s lower boundary thus recedes upwards, as the bed develops, exposing more particles from the original unsheared plug to shear so that they also settle, and this in turn increases the bed thickness. An example of such behavior is given in Figure 11c. Whether a final residual unsheared plug exists or is completely destroyed in the final established flow depends upon the magnitude of ζ.

3.3 Concentration considerations with visco-plastic carrier fluids

The higher viscosity and shear thinning nature of the carrier fluid has an impact on the dilated bed concentration described in §2.1. The packing concentration of the visco-plastic carrier fluids themselves are affected by the applied normal stresses [25], as apparently are beds of coarse particles suspended in such fluids.

Studies in Delft have shown that the coarse particle concentration in the bed adapts itself to the exerted shear stresses [26], where coarse particles, settled from a Couette shear flow, created in an annular flume. Upon increasing the fluid shear stress, the bed compacted more. From considerations of mechanical equilibrium, the shear stresses in the bed are higher than within the flow and the imposed fluid shear stresses are larger than the yield stress, outside of any unsheared plug (which has been shown to exist above the bed). Then, since the strength of the bed increases with solids’ concentration, this concentration will increase until bed strength equals the imposed fluid shear stresses [27]. Such analysis has been successfully applied to flow in flumes, tailings deposits, pipelines and computational studies [23, 28, 29, 30].

Experimentally obtained values of Cb, or values derived from analysis, are typically 10 to 20% lower than those obtained in §2.1.

3.4 Two-layer considerations for coarse suspensions in non-Newtonian carrier fluids

As before, only a simple two-layer model will be considered in this section and the reader is referred to the chapter on pipeline modeling for more advanced models. Since the behavior, when the flow is turbulent, is similar to Newtonian based systems, varying only in detail concerned with the calculation of wall stresses and the extent of particle suspension, only laminar flow processes will be considered here (see e.g., [31, 32, 33]).

The increase in viscosity of the carrier fluid increases the various stresses, and modifies the ways the bed is transported, in particular, it is now possible to convey under conditions where the carrier fluid is in laminar flow.

Changing the rheology of the carrier fluid has profound effects on the bed’s behavior as illustrated here.

The example shown in Figure 12a is based loosely on data obtained at a diamond mine, where -6 mm grits were conveyed using thickener underflow to the TSF [34] for thickened central disposal. It demonstrates the effect of changing the viscosity of the carrier fluid. In this case the actual carrier fluid was well described by the Bingham plastic model $\left(\tau ={\tau }_{\mathit{yB}}+\eta \dot{\gamma }\right)$, where τ_yB and η are the Bingham yield stress and plastic viscosity respectively, and τ and $\dot{\gamma }$ the shear stress and shear rate. This model will be used for illustration without any loss of generality. Increasing the viscosity by increasing the yield stress of the carrier, without changing the plastic viscosity, reduces the extent of the deposition locus, such that, for this system, at yield stress values exceeding 55 Pa, the deposition locus has been totally suppressed. Under these circumstances, the coarse solids will move within the pipe as soon as there is any flow. Such a system cannot be blocked. It is worth noting that the disposal system on which this example is based was designed for a carrier yield stress of 50 Pa, very close to this value. It should also be noted that this reduction in the deposition locus is not solely a function of yield stress. Increasing the viscosity through other means, e.g., modifying η, will have similar effects.

Figure 12.

The effect of yield stress on the deposition locus.

3.4.1 Un-blockable systems

The yield stress to ensure that the solids will move as soon as there is flow is obtained by equating the driving and resisting forces on the bed at incipient motion above the bed. At this point on the plane of symmetry, the stress at the pipe wall and the top of the bed will be equal to the yield stress of the fluid, as will the stress under the bed, since it is not moving. Approximating the flow above the bed to that of flow through an equivalent pipe of diameter equal to the hydraulic diameter of the area above the bed [35], it can be shown that the minimum yield stress required to ensure bed motion at all velocities for arbitrary solids’ concentration can be written as

$${\tau }_{ymin}=\frac{\pi D^{2}F\left(\beta ,f\right)\mathit{Cbg}{\mu }_s\left({\rho }_s-{\rho }_f\right)\left(A-1\right)}{4\left(\mathit{\pi \beta }+Dsin\left(\beta \right)-\frac{\pi D^2\left(A-1\right)}{\mathit{Dh}}\right)}$$E9

where the area above the bed is $A=1-\left(\beta -sin\left(\beta \right)cos\left(\beta \right)\right)/\pi$ and the hydraulic diameter is given by$\mathit{Dh}=D\left(\pi -\beta +sin\left(\beta \right)cos\left(\beta \right)\right)/\left(\pi -\beta +sin\left(\beta \right)\right)$.

Figure 13 demonstrates that for visco-plastic systems, in common with their Newtonian counterparts, the highest deposition velocity occurs at a relatively low concentration (Cv of order 10%), and that this value is a very weak function of yield stress. Substituting this value into Eq. (9) produces a minimum yield stress requirement of 53 Pa, which is consistent with that shown in Figure 12. Satisfying though this result is, it is somewhat academic as experience gained in the laboratory and field has shown that restart is not an issue with visco-plastic systems, providing the deposition velocity is within the laminar flow regime. This is probably due to the inability of the laminar flow to resuspend the particles and produce blockages, although reports of viscous resuspension indicate a mechanism that might [36, 37].

Figure 13.

Deposition velocities as a function of reduced concentration and carrier fluid yield stress for the system shown in Figure 12. Approximate concentration corresponding to the maximum deposition velocities shown dashed.

3.4.2 Turbulent bed erosion

While this section is primarily concerned with flow that appears to be laminar, there are reports of fine particle beds being resuspended through turbulent action above the bed, before the bed is moved en masse under “laminar” flow and this is now examined.

The velocity displayed in Figure 12 is the bulk velocity, i.e., $V=4Q/\left(\pi D^2\right)$, but at deposition, all of fluid flow occurs either above the bed or percolates through the bed. Percolation through the bed is very low with these viscous carriers and so may be ignored. Thus, the velocity above the bed is simply

$$V_a={\left(\frac{D}{D_h}\right)}^2{V}_{\mathit{dep}}$$E10

Many workers (e.g. [38, 39]) have found that for visco-plastic fluids, in particular those modeled using a Bingham plastic, the transition velocity, V_tB, for pipeline flow is insensitive to pipeline diameter and can be approximated by

$$V_{\mathit{tB}}\approx k_t\sqrt{\frac{{\tau }_{\mathit{yB}}}{{\rho }_c}}$$E11

where 22 < k_tB < 26, τ_yB is the Bingham yield stress and ρ_c the carrier fluid density.

For small pipes, less than 150 mm, this simple relationship, breaks down. Values for Vt, obtained from the intersection of the appropriate laminar curves and turbulent predictions (e.g. [40]) produce increasingly higher values as the diameter reduces. Nevertheless, the point at which flow above the bed becomes turbulent will be defined here as when V_a, given by Eq. (10) exceeds that produced by Eq. (11), since this produces a more conservative result. Calculations of these velocities for a moderately viscous carrier fluid, transporting 3 mm solids, is shown in Figure 14.

Figure 14.

Variation of the velocity above the bed, Va, for various pipe sizes compared with the transitional velocity range given by Eq. (11) with the limiting values of k_tB.

The conclusion to be drawn from Figure 14 is that, even for only moderately viscous carrier fluids, the flow will not become turbulent before the deposition velocity is exceeded, except for large pipes, and then only for low to moderate coarse concentration flows, not for high concentration flows, where the flow will remain laminar.

3.4.3 Testing requirements

At the time of writing, 2-layer model predictions for non-Newtonian carrier-based systems require pipeline or laboratory tests to determine suitable values for Cb and the coefficient of sliding friction. Once obtained however, predictions of industrially sized systems can be made typically to within ±10%.

3.5 Comparison with conventional conveying

The thickened tailings of Figure 12a will be used as an example, noting that in this case all the solids, both the -6 mm grits and particles that are contained within the thickener underflow are to be disposed. The concentration of the grits was only 10% v/v but when combined with the carrier slurry the total concentration of the solids was 40.5% v/v. While this concentration may be within the range of conventional conveying, it must be remembered that the carrier fluid is a highly thickened slurry, a requirement for the central discharge method employed on the TSF. The transport characteristics for this suspension were very flat, requiring a pressure gradient of 0.97 kPa/m to produce velocities ranging from 0.5 to 3 m/s within the pipe. Using Eq. (6) and based on these values the SEC is found to be 0.4 kWhr/(tonne km).

Using conventional conveying, based on a mean particle size of 3 mm, at this total concentration, would require the solids to be conveyed in excess of 6 m/s and require a transport pressure gradient of around 1.55 kPa/m, giving an SEC of 0.64 kWhr/(tonne km).

By using a non-Newtonian carrier, the solids are transported using only 62% of the energy consumption, which would otherwise be required, and the suspension can be used as a thickened discharge. Conversely, using conventional conveying techniques would produce a very erosive environment, and require construction of a, now deprecated, conventional TSF.

3.6 What constitutes a coarse particle?

Earlier, it was suggested that coarse particles may be those larger than 0.5 mm, but tests conducted with some broad size distribution uranium tailings [41] indicated that it was only particles less than 40 μm that contributed to the carrier fluid’s rheology, the rest being coarse and reporting to the sliding bed. Carrier fluid rheology is of course material specific, but it is most likely that similar lower limits exist for other mineral slurries.

4. Discussion and conclusions

Two forms of high concentration conveying have been described, both of which enable very coarse particles to be conveyed at low velocities, and in such a way that stopping and starting the flow is easy. While normally requiring higher transport pressure gradients than those required by fine particle flows, their high solids’ concentrations result in low SECs. They both have very low minimum conveying velocities, if any at all, allowing solids to be conveyed at low velocities and providing very large turn down ratios. The low velocities also means that pipe wear and particle attrition is similarly low.

The first form, using water, or similar, as the carrier fluid, has the advantage that separation of the solids from the carrier fluid is simple and does not require facilities to manufacture a special non-Newtonian carrier fluid. However, there are considerable restrictions on the solids that can be pumped, requiring both a broad size distribution and a high, but limited, range of solids’ concentrations, 0.75 < Cv/Cb < 0.9. These restrictions are beyond the capabilities of normal centrifugal or positive displacement pumps and require specialized feeding systems.

The second form employs a visco-plastic carrier fluid. This ameliorates or removes the PSD and concentration restrictions of the former method and has the advantage that it can be transported using conventional pumps. However, unless the material to be pumped naturally forms a suitable carrier fluid, e.g., contains a high clay content or has a friable component, equipment and techniques are required to produce the necessary carrier and maintain appropriate rheological characteristics during normal lifetime process variabilities. Separation of the coarse material from the carrier, if required, can be costly and involved, although sheared settling, described above, can be exploited to assist in this. Disposal of the used carrier material may also be problematic. Where separation is not required or desirable, e.g., waste disposal, the presence of a yield stress in the carrier fluid means that deposits are stable. Distribution of these suspensions across a TSF can no longer rely on the simple ring main distributions of conventional TSFs, and requires single or multiple central discharge systems to be employed.

Both means of conveying are successfully characterized and predicted using layered models, which provide a mechanistic means to scale up from test data with confidence.

Acknowledgments

The author would like to thank the CSIRO’s Division of Mineral Engineering and Advanced Fluid Dynamic Laboratory, for support in this work, to Dr. Lachlan Graham, in particular, for his imaging of many of these flows, and assistance in developing a deeper understanding their behavior and to Dr. Arno Talmon for his insights into the bed structure when using non-Newtonian carriers.