Tim Fitton, ATC Williams - Self formed channels in tailings disposal
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Tim Fitton, ATC Williams - Self formed channels in tailings disposal

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Tim Fitton, Tailings Engineer, ATC Williams presented this at the 3rd Annual Slurry Pipeline Conference. The Conference focuses on the design, construction, operation and maintenance of mineral slurry ...

Tim Fitton, Tailings Engineer, ATC Williams presented this at the 3rd Annual Slurry Pipeline Conference. The Conference focuses on the design, construction, operation and maintenance of mineral slurry pipelines.

For more information, visit http://www.informa.com.au/slurrypipelineconference

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    Tim Fitton, ATC Williams - Self formed channels in tailings disposal Tim Fitton, ATC Williams - Self formed channels in tailings disposal Document Transcript

    • Fitton – Self-formed channels in tailings disposal Third Annual Slurry Pipelines Conference, Perth 2013 Self-formed channels in tailings disposal Tim Fitton - ATC Williams Abstract Self-formed channel occur in nature, wherever the flow of a fluid shapes the open channel in which it is travelling. Rivers, mudflows, lava flows and glaciers are examples of this. Tailings slurry (mine waste mixed with water) is typically hydraulically discharged into large impoundments for its disposal, though in recent decades new technology has been applied to thicken the slurry to form deposits with gently sloping “beaches” (surfaces), allowing the tailings to be stored more efficiently. The discharge of a tailings slurry into a tailings disposal area will result in the slurry being transported along self-formed channels across the beach. Such channels are normally turbulent, but occasionally they are laminar with a plug flow mechanism. It has been observed that such channels can be grouped into three regimes; segregating turbulent flow, non-segregating turbulent flow, and non-segregating plug flow. This paper presents three different methods of predicting the headloss in a self-formed channel on a tailings beach, to cover each of the three tailings deposition regimes that are encountered. Each of these three methods has been found to be of use in the prediction of tailings beach slopes. 1 Introduction A self-formed channel is a gravity-flow open channel with its cross section and course shaped by the fluid that flows along it. Such channels are common in nature, with the most obvious example being rivers. Glaciers, mudslides and lava flows are some other examples. The water flowing in a river will erode the river bed in some areas and deposit sediments in other areas. Most of the erosion takes place in the upper reaches of the river, where the gradient of the stream is steep enough to induce high velocity flow. Conversely, deposition of sediments mainly occurs in the river delta at the lower reaches of the river, where the velocity diminishes rapidly with the chaotic mixing of the river outflow with the stiller waters of the sea. In the mid-section of a river, there is a more even balance between erosion and deposition. In this paper, such conditions are labelled as “equilibrium flow”. At all points along a river, the cross section is being shaped by the flowing water, which in turn causes the river to gradually alter its course over time. Due to the low viscosity of water, rivers always flow in the turbulent regime. The turbulent eddies carry the sediment particles, and often sweep up others. 1
    • Fitton – Self-formed channels in tailings disposal The mechanics of a lava flow are very different to that of a river, despite both natural processes featuring a fluid that forms its own channel shape and course. In the case of a lava flow, the fluid is very viscous, and it also develops a yield stress as it cools. Lava flows do not erode the underlying material to the same degree as a river, and typically a lava flow channel is beset by stationary lava that stopped only hours or days beforehand. Tailings is waste from the mining industry. It is typically sand and silt that has been artificially created through the process of digging or blasting rock from the earth, and then mechanically crushing and grinding it to the optimum size for the extraction of the target mineral. Depending on the type of mine and mineral extraction process in use, the tailings may contain introduced chemicals. Occasionally tailings is radioactive. Depending on the chemistry of the original rock, the tailings may also generate acid if it is susceptible to oxidation upon contact with the air. For all these reasons, it is generally accepted that tailings should be disposed of in environmentally responsible manner. The quantity of tailings that is produced by a small mine could be 500,000 tonnes per year, whilst a large mine might produce as much as 40 million tonnes per year. There are a few huge mines that produce more than 100 million tonnes per year, and it is expected that the number and sizes of mines will continue to grow in time. The disposal of such large quantities of tailings is a significant concern. Typically this has been achieved by constructing a dam to form an impoundment of some sort, and then filling up the impoundment with hydraulically transported tailings (tailings and water slurry pumped through a pipe or gravity fed along an open channel). The tailings particles settle out in the impoundment to form a deposit, the surface of which is called a beach. Segregation of the tailings particles is typical in such impoundments, with the coarse particles depositing nearer to the discharge point. In more recent years Eli Robinsky’s concept of thickened tailings disposal (Robinsky 1975) has been progressively taken up as an alternative to the traditional impoundment disposal method (Williams et al. 2008). Robinsky’s concept involves the discharge of a tailings slurry that is thickened beyond the point of segregation. Such non-segregating slurries form beaches with steeper overall slopes, which can be exploited to use much smaller embankments for containing the same volume of tailings. Robinsky’s concept also provides other benefits such as reduced water usage, reduced seepage of contaminants into the ground, and greater stability of the tailings deposit, but such matters are beyond the focus of this paper, and have been well documented elsewhere (Fourie 2012). On thickened and conventional tailings deposits alike, it is typical to see self-formed channels of tailings slurry flowing across a tailings beach. These channels form naturally as the slurry adopts a path of least resistance towards its active deposition area. At the downstream end of the channel, the slurry will spread out in a sheet in the deposition area. Over time the downstream end of the channel will gradually advance across the sheet, making the channel grow in length. This will continue until such time as the sheet depth 2
    • Fitton – Self-formed channels in tailings disposal builds up too much, at which time it will present a greater resistance to the incoming channel flow. Almost instantly, the tailings slurry will “break out” of its self-formed channel at some point upstream and form sheet flow elsewhere, and in the following minutes a new channel will start advancing across that new sheet. This process sees the channel course change periodically. An inspection of a tailings beach will reveal hundreds of dry “extinct” channels that were left abandoned by the slurry as it broke out at some point upstream. It is evident from this process that it is the channel slope that dictates the overall slope of the tailings beach. Such channels on tailings beaches are typically flowing under equilibrium flow conditions, such that deposition and erosion are effectively cancelling one another out. The slope of a channel with equilibrium flow conditions is labelled the “equilibrium slope”. A photograph of a self-formed channel on a tailings beach is presented as Figure 1. Figure 1 A self-formed channel on a tailings beach (Tailings Info website) Prior to the introduction of Robinsky’s thickened tailings concept there was little interest in tailings beach slopes, since tailings beaches typically exhibited overall slopes of about 0.1 to 0.3%, allowing engineers to design storage impoundments without too much fuss. Since the adoption of Robinsky’s thickened tailings concept however, the mining industry has been far more interested in predicting the slope of the beach, since the resultant overall beach 3
    • Fitton – Self-formed channels in tailings disposal slopes have varied from 0.5% to 5.0% from one mine site to another. An inaccurate prediction of a beach slope could cost a mining company millions of dollars in the construction of the dams and pumping infrastructure that do not suit the particular thickened tailings disposal. It was this mining industry interest in beach slope prediction that led us to equilibrium slopes of self-formed channels on tailings beaches. 2 Segregating slurries A self-formed channel on a tailings beach is not unlike a river, particularly in situations where segregating tailings slurry is being discharged. Turbulent eddies in the channel carry the tailings particles along, as is seen in a river. However, the segregating slurry may be concentrated enough to exhibit non-Newtonian viscous characteristics, so it is necessary to take the slurry rheology into account if one is attempting to model its behaviour. Fitton (2007) presented an a-priori model that enabled the prediction of the channel equilibrium slope for segregating slurries. (“A priori” is a Latin term meaning “from the earlier”. It is used to describe an equation that is based on previously published equations, without introducing any new empirical factors.) The model featured equations from the fields of non-Newtonian open channel flow, sediment transport and rheology: The slope of an open channel with uniform flow can be calculated with the Darcy-Weisbach equation: S0 = f . V2 8 gRH (1) where S0 is the slope of the channel bed under uniform flow conditions, RH is the hydraulic radius, V is the average velocity of flow, g is the acceleration due to gravity and f is defined as the Darcy friction factor. The open channel form of the Colebrook-White equation will be used to calculate the Darcy friction factor:  ks 1 2.51 = −2 log10  + f 14.8 RH Re f      (2) Of key interest in this work is the ks parameter, which represents the roughness of the pipe or channel walls (expressed in meters). The value of 2 x d90 has been adopted for estimating ks on the basis of work done by Ikeda et al. (1988). The Re parameter in the Colebrook-White equation is the Reynolds Number. Haldenwang et al. (2004) presented the following equation for calculating the Reynolds number for Non4
    • Fitton – Self-formed channels in tailings disposal Newtonian turbulent open channel flow, with the rheological properties of a fluid of density ρ expressed in terms of the three Herschel-Bulkley fitting parameters τy, K and n: Re HB = 8ρV 2  2V  τy + K   RH  n (3) From numerous experimental studies into the transport of sediments in turbulent flows, there are many equations presented in the literature that enable the prediction of the minimum average velocity required to keep particles in suspension in a pipe (VC). This particular velocity appears in the literature under several names, with the most common ones being “minimum transport velocity”, “deposition velocity” and the “critical velocity”. Fitton (2007) investigated the performance of 16 minimum transport velocity equations from the literature. It was found that the Wasp et al. (1977) equation performed quite well for segregating slurries, which is expressed below in an open channel form: VC = 3.8CV 1/ 4  d   4R  H     1/ 6  8 gRH ( ρ s − ρ l )    ρl   1/ 2 (4) where d is the median particle diameter, CV is the slurry concentration by volume, ρs is the density of the solid particles and ρl the density of the carrier fluid. In order to determine an equilibrium slope the channel cross-sectional shape needs to be defined in such a way that the hydraulic radius can be calculated as a function of the depth. Fitton recommended a parabola with a width 5.5 times the depth, based on some experimentally measured data. To predict an equilibrium slope an iterative process was used to arrive at a unique channel depth that produced a transport velocity that was equal to the average velocity in the channel. At this point, a slope could be calculated. 3 Non-segregating slurries without plug flow Fitton (2007) also presented an empirical equation for the prediction of the minimum transport velocity of a non-segregating slurry, based on two sets of field data that he had generated in flume experiments at the Sunrise Dam gold mine in Western Australia and the Peak gold mine in New South Wales: 5
    • Fitton – Self-formed channels in tailings disposal  ρVRH VCNon−segregating = 0.145 ln  K  BP     (5) In equation 5, the KBP parameter is the plastic viscosity of the slurry. The same prediction method could be applied as for segregating slurries, except with the use of equation 5 instead of equation 4. 4 Non-segregating slurries exhibiting plug flow In 2011 a pilot plant trial was carried out at the Chuquicamata copper mine in Chile to investigate the characteristics of the local copper tailings at higher levels of thickening. (Engels et al 2012, Pirouz et al 2013) The pilot plant featured a tall pilot scale thickener that could be used to produce batches of high concentration slurry. During those trials it was discovered that a non-segregating slurry could be thickened to such a degree that its self-formed channels behaved more like a lava flow than that of a river, since the viscosity and yield stress of some batches of slurry were high enough to induce plug flow conditions in the channel. (Fitton and Slatter, 2013) Plug flow occurs when a portion of the slurry in the channel remains unsheared. This is illustrated in Figure 2. Figure 2 Open channel plug flow observed in tailings Fitton and Slatter (2013) presented a method for analysing such channels. They adopted a half ellipse instead of the parabola that had previously been assumed by Fitton. It was proposed that half an ellipse is a more realistic cross sectional shape for a self-formed channel, particularly at the banks of the channel, where the sharp points of the parabola are deemed to be unrealistic compared to the vertical up-turns of the ellipse. Diagrams are presented in Figure 3 to show the distribution of shear stress and velocity in pipe and channel centrelines in laminar flow, highlighting the impact of yield stress fluids. 6
    • Fitton – Self-formed channels in tailings disposal Figure 3 Distribution of shear stress and velocity in laminar pipe flow (top) and laminar open channel flow (bottom) A number of assumptions were proposed for the open channel plug flow model: • • • Flows in the sheared zone are laminar, with parabolic velocity profiles The channel cross section is a half ellipse The plug is also a half ellipse, with the same width to depth ratio as the greater channel In developing their plug flow model, Fitton and Slatter adapted pipe flow equations presented by Slatter (1997) to cater for open channel flow. To calculate the depth of the plug, the following relationship was presented: τ  d P =  Y d τ W  (6) where dP is the depth of the plug at the channel centreline and d is the total depth at the centreline of the channel, as shown in Figure 2. 7
    • Fitton – Self-formed channels in tailings disposal The Re3 Reynolds number was modified using the laminar pipe/channel conversion D = 4RH: Re 3 = 8 ρVSZ 2  2V τ Y + K  SZ R  HSZ     n (7) Where VSZ is the average velocity in the sheared zone and RHSZ is the effective hydraulic radius of the sheared zone. To calculate RHSZ, the following equation was presented: RHSZ = R H − RHP (8) RH is the hydraulic radius of the channel, and RHP is the hydraulic radius of the plug. VSZ is calculated: VSZ = QSZ ASZ (9) Where QSZ is the flow rate in the sheared zone and ASZ is the cross sectional area of the sheared zone. QSZ is calculated as follows: QSZ = Q − QP (10) where QP is the flow rate in the plug, equal to (11) QP = u P . AP with uP as the velocity of the plug and AP as the cross sectional area of the plug. To determine the plug velocity a geometric approach was taken, as illustrated in Figure 4. 8
    • Fitton – Self-formed channels in tailings disposal Figure 4 Velocity profiles for a plug flow scenario; the green line shows the actual velocity profile, while the blue line shows the average velocity. The area contained inside both shapes is identical by definition. The two velocity profiles shown in Figure 4 contain the same area. By this paradigm the plug velocity (uP) can be determined by equating the areas inside the two shapes as follows: V .d = u P d P + 2 u P (d − d P ) 3 (12) Strictly speaking, equation 12 is only accurate for an infinitely wide channel. To address this, the respective hydraulic radii were substituted for the centreline depths to make equation 12 accurate for a three-dimensional channel. Making uP the subject yields: uP = RHP V .RH + 2 ( R H − RHP ) 3 (13) The wall shear stress is required for the determination of the plug depth (equation 6). In channel flow this is typically calculated using DuBoys equation, but in this particular situation that is not helpful because the channel slope is required as an input parameter, and that is what is ultimately sought to predict. Instead the problem is approached by applying with the fundamental relationship between the shear stress (τ), apparent viscosity (η) and shear rate (γ̇): τ = η .γ& (14) 9
    • Fitton – Self-formed channels in tailings disposal The shear rates in the channel can be calculated by deriving the quadratic equation for theoretical velocity distribution profile in the sheared zone (note that this parabolic velocity distribution is valid for a Bingham plastic, and will be approximate for a Herschel-Bulkley). The velocity profile can be described as follows: u = uP − uP (depth − d P ) 2 2 (d − d P ) (15) The derivative of equation 15 is the shear rate function. Deriving equation 15 and making the depth equal to the maximum depth (d) yields the shear rate at the channel bed (γ̇W): γ&W = 2u P (d − d P ) (16) Substituting the respective hydraulic radii for the centreline depths to make equation 16 accurate for a three-dimensional channel gives: γ&W = 2u P ( RH − RHP ) (17) The apparent viscosity is then calculated using the rheological parameters and the shear rate: η= τ Y + K .γ& n γ& (18) This equation completed the channel plug flow model. However, it will become immediately evident in the attempted application of this new model that the plug depth is required as an input parameter for determining the wall shear stress, and the wall shear stress is required for calculating the plug depth. Therefore the plug flow model is implicit as presented. This problem arises from open channel flow possessing an extra dimension over pipe flow in terms of its variable depth, which makes its modelling more complex than that of pipes. An increase in the flow rate in a pipe simply results in an increase in the velocity, for example. In an open channel, an increase in the flow rate will yield an increase in the depth as well as 10
    • Fitton – Self-formed channels in tailings disposal the velocity, particularly where non-Newtonian fluids are involved. As a result of this added variable, an iterative solution is required. It was found that initially estimating the wall shear stress to be equal to 1.2 times the yield stress enabled a convergent iterative solution to four significant figures to be successfully reached after six iterations. With the use of a computer spread sheet program, this iterative approach was easily applied. 4.1 Channel aspect ratio The channel plug flow model presented here will enable the modelling of yield stress fluids in open channels of any cross-sectional geometry. However, in the case of self-formed tailings channels, there exists the question of the aspect ratio of the channels. Fitton (2007) carried out a numerical analysis of different width-todepth (w/d) ratios for a limited number of such channels, and after comparing the predicted results against experimentally measured data, recommended 5.5:1. Fitton and Slatter (2013) attempted to back-calculate the width-to-depth ratio (w/d) for each of the selfformed channels that were observed in the Chuquicamata flume trials (Pirouz et al 2013). It was not possible to measure the depth of the self-formed channels during that experimental work, since any disturbance to the channel created by the immersion of a probe would result in the destruction of the fragile channel bed and banks. However, flow rates, plug velocities and channel widths were measured, so it was possible to backcalculate the channel depth. This deduction of channel depths was undertaken, and it was found that the aspect ratios for the 17 measured self-formed channels varied from 2.5 to 11. Due to the considerable range of aspect ratios that were thus calculated for the Chuquicamata flume trials, it was decided that the plug flow model should include an aspect ratio prediction model if any reasonably strong trends could be discovered between the deduced aspect ratio and some of the measureable characteristics of the slurry, rather than simply assuming a constant ratio. Analysis was carried out to identify trends relating the slurry characteristics to the width-todepth ratios calculated for the Chuquicamata data. It was found that a modest trend was observed when the w/d values were plotted against the Bingham yield stress of the slurry. This plot is presented as Figure 5. It is noted that the Bingham fit to each rheogram was tangent to the 100 s-1 point on the curve. 11
    • Fitton – Self-formed channels in tailings disposal Figure 5 Plot of Bingham yield stress vs w/d ratio for the self-formed channels in the Chuquicamata flume trials The equation describing the trend curve that is shown on the Figure 5 plot is as follows: w/ d = 25 τ yB (19) This equation was adopted for predicting channel aspect ratios for self-formed channels in the plug flow model. 4.2 Elliptical geometric equations In order to apply the plug flow channel model to an elliptical channel shape it is necessary to calculate the cross sectional area and the wetted perimeter of a half ellipse such as that shown in Figure 2. The following equation can be used to calculate the area of the half ellipse: A= πdw 4 (20) 12
    • Fitton – Self-formed channels in tailings disposal Ramanujan (1914) presented an excellent approximation for calculating the circumference of an ellipse. It has been modified here for calculating the wetted perimeter of the half ellipse:   π  P = (w / 2 + d ).1 + 2  10 +      2   w/2 − d   4 − 3   w/2 + d     w/2 − d  3   w/ 2 + d  2 (21) It is noted that equations 20 and 21 can also be used to calculate the area and wetted perimeter of the plug (AP and PP) if the plug depth and plug width are used instead of the overall channel depth and width respectively. 4.3 Predicting a beach slope with the plug flow model The overall approach is similar to the a priori beach slope model previously presented, but the plug flow model adds some more steps to the process. The application of the model remains the same – the channel depth is adjusted until the channel velocity is equal to the predicted minimum transport velocity. The Fitton 2007 non-segregating minimum transport velocity equation (equation 5) is recommended for use in the plug flow beach slope model. 5 Conclusion The discharge of a tailings slurry into a tailings storage facility will result in the slurry forming its own channels across the beach. Such channels can be laminar or turbulent. It has been proposed that these channels can be grouped into three regimes; segregating turbulent flow, non-segregating turbulent flow, and non-segregating plug flow. This paper has presented a method for predicting the equilibrium slope of a self-formed channel on a tailings beach for each of these three regimes. It has been found that each of the three methods has its use in the prediction of tailings beach slopes. References Fitton, T.G. (2007) Tailings beach slope prediction, PhD thesis, RMIT University, Australia (Since published as a book by VDM Verlag, Saarbrucken, Germany in 2010). Fourie, A.B. 2012, Perceived and realised benefits of paste and thickened tailings for surface deposition, paper presented to Paste 2012, Sun City, South Africa, 2012. Pirouz, B., Seddon, K.D., Williams, M.P.A., Echevarria, J. & Pavissich, C. 2013, Tilt flume testing for beach slope evaluation at Chuquicamata Mine CODELCO-Chile, paper presented to Paste 2013, Belo Horizonte, Brazil 13
    • Fitton – Self-formed channels in tailings disposal Ramanujan, S., 1914, Modular equations and approximations to Pi. Quart. J.Pure. Appl. Math. 45 (1913-1914), 350{372. Robinsky, E.I. 1975, 'Thickened discharge - A new approach to tailings disposal', CIM Bulletin, vol. 68, pp. 47-53. Slatter, P.T. 1997, The effect of the yield stress on the laminar/turbulent transition, 9th Int. Conf. Transport and Sedimentation of Solid Particles, Crakow, Poland, 1997. Tailings Info website, accessed 11 Nov 2013. http://www.tailings.info/disposal/paste.htm Wasp, E.J., Kenny, J.P. & Gandhi, R.L. 1977, Solid-liquid flow slurry pipeline transportation, First edn, Trans Tech Publications, Germany. Williams, M.P.A., Seddon, K.D., & Fitton, T.G. 2008, “Surface Disposal of Paste and Thickened Tailings - a brief history and current confronting issues”, paper presented to Paste 2008, Kasane, Botswana, 6-9 May, 2008. 14