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Changes in underflow solid fraction and yield stress in paste thickeners by circulation

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  • Corresponding author:

    Ai-xiang Wu    E-mail: wuaixiang@126.com

  • Received: 12 November 2019Revised: 1 September 2020Accepted: 2 September 2020Available online: 3 September 2020
  • The trouble-free and efficient operation of paste thickeners requires an optimal design and the cooperation of each component. When underflow discharging is suspended, alleviating the vast torque that the remaining solids within the thickeners may place on rakes mainly lies in the circulation unit. The mechanism of this unit was analyzed, and a mathematical model was developed to describe the changes in underflow solid content and yield stress. The key parameters of the circulation unit, namely, the height and flow rate, were varied to test its performance in the experiments with a self-designed laboratorial thickening system. Results show that the circulation unit is valid in reducing underflow solid fraction and yield stress to a reasonable extent, and the model could be used to describe its efficiency at different heights and flow rates. A suitable design and application of the circulation unit contributes to a cost-effective operation of paste thickeners.
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Changes in underflow solid fraction and yield stress in paste thickeners by circulation

  • Corresponding author:

    Ai-xiang Wu    E-mail: wuaixiang@126.com

  • 1. Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing 100083, China
  • 2. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
  • 3. Shandong Taikai Power Electronic Co., Ltd., Taian 271000, China

Abstract: The trouble-free and efficient operation of paste thickeners requires an optimal design and the cooperation of each component. When underflow discharging is suspended, alleviating the vast torque that the remaining solids within the thickeners may place on rakes mainly lies in the circulation unit. The mechanism of this unit was analyzed, and a mathematical model was developed to describe the changes in underflow solid content and yield stress. The key parameters of the circulation unit, namely, the height and flow rate, were varied to test its performance in the experiments with a self-designed laboratorial thickening system. Results show that the circulation unit is valid in reducing underflow solid fraction and yield stress to a reasonable extent, and the model could be used to describe its efficiency at different heights and flow rates. A suitable design and application of the circulation unit contributes to a cost-effective operation of paste thickeners.

    • Sedimentation operations are crucial for water recovery in industries, such as mineral processing, sewage disposal, and metallurgy [12]. The emphasis on a well-clarified overflow or a highly concentrated underflow brings the operations into two different areas: clarification and thickening. In the mining industry, thickeners have been widely used as equipment due to their continuous and stable operational capacity in tailings thickening. They have gained rapid development particularly with the popularization of the cemented paste backfill (CPB) technology, for which the highly concentrated underflow is the key material to produce the paste [34].

      The CPB technology has been well operated in underground mines worldwide because it could fill a large proportion of the tailings (up to 60%) back into the underground mined-out areas [57], not only preventing surface subsidence but also alleviating environmental and safety risks caused by surface tailings ponds [89]. Typically, the tailings generated by mineral processing plants are first thickened to a designed content (i.e., 70wt%–85wt%) and then mixed with a hydraulic binder with a dosage of 3wt%–7wt% in a surface backfill plant to produce the CPB [1012]. The fresh CPB is then transported by gravity and/or pumped through pipelines to underground mine excavations. Interested readers can refer to Ref. [1314] for a detailed explanation of the CPB technology. To prepare the CPB of a desired consistency, the underflow should meet the requirements on solid content (typically 70wt%–85wt%) [1516].

      The demands on high underflow concentration have driven thickeners into continuous evolvement. With the use of flocculants, conventional thickeners have been developed into high- or ultrahigh-rate thickeners. The further enhancement of the underflow into largely nonsettling, nonsegregating paste results in paste thickeners (deep-cone or deep-bed thickeners of same meaning according to different terminology used by manufacturers) [1718], which are generally designed to produce underflow of a yield stress above 100 Pa [1920].

      In practical CPB operations, the performance of paste thickeners needs to be reasonably steady with underflow of a desirable and sustainable consistency [2123] and must meet the demands of underground mining and backfilling schedule. Therefore, underflow discharging is not always continuous and may temporarily be suspended and soon restarted in accordance with backfilling needs. When in pauses, the tailings are likely to undergo a relatively long bed residence time in the thickener. Underflow density is generally recognized to be a function of the bed residence time (time that solids spend in the thickener bed) among other factors. Typically, residence for paste thickeners takes several hours [19], and excessive residence of one or several days leads to a dramatical increase in the underflow solid fraction as a result of enhanced settlement and consolidation under self-weight and shearing [24]. Moreover, a high solid fraction underflow requires a high stress to yield. This requirement can place a great deal of torque on rakes within thickeners [25] or even cause rake failure, which hinders underflow discharging when backfilling restarts; thus, the mining schedule is affected.

      Generally, two approaches are proposed to alleviate this situation: setting up a rake unit or a circulation unit. The rake, a distinguishing characteristic of paste thickeners, can improve the consistency and fluidity of the slurry by mixing and shearing actions through its rotations [2627]; its mechanism and design have been studied and highlighted [2829]. However, the effect of shear in the dewatering of sediments could not be ignored, and it has limited capacity in stabilizing the slurry fluidity under special conditions, such as during backfilling pauses. By contrast, the circulation unit works in a completely different way by pumping underflow from the bottom to the upper levels within the thickener to stabilize bottom solid content and avoid over-compaction during long-time residence. The use of the unit contributes to a successful operation of paste thickeners under abnormal conditions, and relative studies are of practical importance. However, only a few studies have been conducted on the effect of the circulation unit on the underflow solid content and its mechanism [30]. Moreover, the effect of the circulation parameters on the performance has not been investigated.

      In this study, the authors conducted a pilot-scale study on the circulation unit by using a self-designed laboratorial thickening system, which is assumed to bring the solid fraction profile closer to uniformity and then produce a massive effect on the yield stress. A model was theoretically developed to describe this situation along with experiments. The experimental results show a decrease in underflow concentration and its yield stress, and the model could describe the circulation mode to a reasonable extent. With increasing emphasis on thickening in the CPB technology, the circulation unit and its model contribute to an improved operation of paste thickeners.

    2.   Circulation operations
    • With changes in its geometry, thickeners have evolved over time to become more efficient, as shown in Fig. 1. Paste thickeners use a deep tank for compression (a typical 30º–45º tank cone and high-torque raking system) to produce high-density underflow. The trouble-free operation of this system is of practical importance, and any failure results in time-consuming maintenance. Therefore, an effective method to keep the fluidity of the remaining slurry within paste thickeners during backfilling pauses is essential.

      Figure 1.  Evolution process of paste thickener [19].

      In paste thickeners, the solid content increases greatly at the bottom under large compression [31], and the circulation aims to pump the most thickened portion to upper levels and enable solids to move vertically [32]; thus, the long-time residence of tailings particles at the bottom is prevented. When discharging is suspended together with the tailings feeding, the remaining suspension undergoes circulation through external pipes and by pumping, as illustrated in Fig. 2. The circulation height could be designed and selected in accordance with the practical needs and costs. When the underflow concentration is relatively low and the backfilling restarts shortly, a smaller height could be applied; by contrast, a larger height is used in consideration of actual needs and economical costs. Currently, the operation of the circulation unit entirely depends on practical experience, and its mechanism has yet to be studied from a theoretical perspective.

      Figure 2.  Schematic of an underflow circulation unit in paste thickeners.

    • The thickening process refers to the content of suspended solid particles by gravity settling and shearing; it could be deemed as a transition between three phases or zones: the free settling, hindered settling, and compression zones [33]. The main difference is the change in solid distribution. The operation of paste thickeners in the circulation mode generally happens in the compression zone. The authors assume that the solid volume fraction is approximated to be a nearly linear distribution on the vertical direction in the compression zone of the pilot-scale thickener [34]. At any given height, h, the volume fraction, Cv, could be approximated as

      where Cv is the solid volume fraction, vol%; Cv,0 is the volume fraction at the point of 0, vol%; k is the rate of volume fraction change along the axis z, m−1; h is the distance from the point 0, m.

      The involved circulation area is assumed to be an inverted cone (the results of the analysis herein are independent of its shape as long as it is regular). On the basis of field practice, the effect of circulation is assumed to be associated with the circulation height, H (the height at which the material is injected back into the thickener), and the pump flow rate during circulation, Q (ml∙min−1). The effect of flow rate is described in the form of f(Q), and as illustrated in Fig. 3, the actual effective height, He, could be expressed as

      Figure 3.  Illustration of the involved circulation zone.

      The total solid volume in the involved circulation area can be calculated by

      where ${V_{\rm{s}}} $ is the total solid volume in the involved zone, m3; Re is the radius of the inverted cone at the effective height He, m.

      With Eqs. (2) and (3), the total solid volume can be further calculated as follows:

      The goal of the circulation mode is to regulate the underflow concentration by continuously recycling the underflow back to the upper levels of the thickener until it brings the solid fraction profile closer to uniformity. After a period of circulation, the initially spatially nonuniform solid distribution in the involved zone comes to reach a dynamic balance; hence, the fluidity of underflow is stabilized. The solids are assumed to be of a homogenous and uniform distribution in the involved circulation area, and thus the balanced tailings volume fraction, $ {\bar C_{\rm{v}}}$, is expressed as follows:

      where V is the volume of the involved zone, m3.

      Eq. (5) could also be described as follows:

      where $\Delta {C_{\rm{v}}}$ is the change in the underflow volume fraction between the initial state and the stabilized state.

      A formula relating the volume fraction to solid content of slurries could be described as follows:

      where ${C_{\rm{w}}}$ is the solid content of the underflow, wt%; ${\rho _{\rm{s}}}$ is the solid density, kg/m3; ${\rho _{\rm{w}}}$ is the water density, kg/m3.

      A general relation has been noted between the yield stress (${\tau _0}$) and solid content (${C_{\rm{w}}}$) of the tailings [3536]. The yield stress is a function of solid content and is unique for any given suspension [18]. A power law model shown in Eq. (8) was found for paste backfill material [17].

      where α (Pa) and β are experimentally determined constants; Cw is the solid content (in decimal).

      With the above equations, a mathematical model was developed to describe the changes in the yield stress and concentration of underflow in the pilot-scale paste thickener. In practical backfilling, the model could be beneficial for the regulation of slurry concentration when discharging is suspended to avoid rake failure on the basis of the circulation unit.

    3.   Materials and methods
    • The unclassified tailings used herein were sampled from a copper mine in Sinkiang, China. The tailings size distribution was analyzed by a laser particle analyzer; the wet-sieving method was utilized simultaneously for particles >75 μm. As shown in Fig. 4, the tailings have a reasonable fine particle content (<20 μm), which is essential for the preparation of CPB [3738]. Generally, a proportion of at least 15wt% fine tailings is required for retaining sufficient water to produce the CPB [39].

      The tailings’ specific gravity is 2.662. The coefficient of uniformity CU (18.36) and coefficient of curvature CC (1.62) revealed that the tailings contain a wide range of size distribution and have representations of all dimension fractions. The sampled tailings could be classified as a relatively well-graded material [40]. The chemical characteristics of the tailings (Table 1) were determined by X-ray fluorescence. In the thickening experiments, the flocculant utilized was the synthetic anionic polyacrylamide, Magnafloc 5250, because of its superior performance in practical backfilling operation at this mine.

      Figure 4.  Particle size distribution of the tailings.

      SiO2CaOAl2O3AgMgOSAsCuPbAu
      65.689.306.281.611.420.400.060.050.040.03

      Table 1.  Main chemical composition of the sampled tailings wt%

    • Conventional laboratorial settling experiments are generally conducted to measure cylinders due to its simplicity. However, the results are of limited guidance for practical thickening design. Hence, a continuous laboratorial thickening system was built, as illustrated in Fig. 5. The settling column was 100 mm in diameter and 1000 mm in height, which were designed to minimize wall effects without excessively increasing the feed slurry quantity on a bench-scale and continuous basis [41].

      Figure 5.  Schematic of the laboratorial thickening system. H1, H2, and H3 represent various circulation heights.

      Initially, nine sets of sedimentation (without discharging) were performed as a simulation of the pauses in practical thickening to determine the subsequent experimental factors, namely, the feeding content, feeding flow rate, and rake speed, as shown in Table 2. The factors were selected in accordance with practical operations and the similarity criterion. As the tailings were sampled from the mineral processing plant at a content of 25wt%–30wt% and were generally diluted to 10wt%–20wt% before mixing with the flocculant, the feeding content was designed to be 10wt%, 15wt%, and 20wt%. In terms of the feeding flow rate, the calculation of the solids’ throughput per unit cross-sectional area of the experimental column proposed the range of feeding flow rate to be 156.5–2355.7 mL·min−1; this parameter was set to 400, 600, and 800 mL·min−1 in this experiment. In field practice, the rake speed is typically 0.14–0.3 r·min−1 within paste thickeners. In accordance with the speed scale, this parameter was calculated to be 0.5–11.5 r·min−1 in the experimental device herein. Therefore, it was set to 2, 6, and 10 r·min−1.

      No.Feeding
      content /
      wt%
      Feeding flow
      rate /
      (mL·min−1)
      Rake
      speed /
      (r·min−1)
      Feeding
      time /
      min
      Underflow
      concentration /
      wt%
      T-110400 29075.9
      T-210600 67073.1
      T-310800104574.5
      T-415400 66072.6
      T-515600104070.6
      T-615800 22571.7
      T-720400104469.5
      T-820600 23069.4
      T-920800 62272.1
      Note: Underflow concentration refers to the underflow solid content at 12 h from the beginning of feeding.

      Table 2.  Parameters and results in the sedimentation tests

      For each test, 4 kg of tailings was fed at corresponding contents and flow rates for corresponding feeding times. Then, the feeding was ceased, and the underflow concentration at 12 h from the beginning was recorded (Table 2). Throughout each test, the rake was operated at a corresponding speed. The flocculant was diluted to a content of 0.01wt% and utilized at a dosage of 20 g·t−1 in the pilot-scale thickening process. The results show that the underflow solid content of T-1 tends to be high and likely to cause rake failure. Therefore, the parameters of T-1 were used as the basis to perform subsequent circulation experiments.

    • Before the circulation test, the tailings slurry was thickened in accordance with the T-1 parameters. This thickening process was performed by pumping the tailings slurry of 10wt% solid content at a pump flow rate of 400 mL·min−1. After 90 min, 4 kg of tailings was fed into the thickening system. Then, the feeding was ceased, and the circulation began by returning the underflow to higher levels, as shown in Fig. 5. In the thickening process, the rake speed was set to 2 r·min−1.

      Nine sets of circulation tests were conducted. The two parameters (circulation height and flow rate) were selected in accordance with practical experience in their relationship with the mud bed and feeding and discharging rates. The heights of 140, 240, and 340 mm were set (H1, H2, and H3, respectively, as shown in Fig. 5); for each height, three flow rates, i.e., 200, 600, and 1000 mL·min−1 were tested (Q1, Q2, and Q3, respectively). As soon as each thickening process was completed, a circulation test was conducted, and each circulation was operated for 180 min. The solid content of the underflow was measured every 20 min. The rheological properties of the resulting underflow after circulation were measured.

    • The resulting underflow was sampled and tested by using the Brookfield R/S+ vane rheometer. Vane rheometers are widely accepted as a preferred approach for the rheological characterization of concentrated suspensions, especially for yielding materials [35]. This method has two distinct advantages in yield stress measurement as it enables the yielding to occur within the suspension and minimizes the disturbance caused during immersion of the vane. The instrument could be used in two modes: shear stress-controlled and shear rate-controlled modes. In the latter, flow curves based on the obtained stress to rate data could be analyzed by applying the constitutive equations (linear relationship: Bingham model, nonlinear relationship: Herschel–Bulkley model and Casson model) or through extrapolation to the zero shear rate [42]. In this study, the controlled shear rate mode was adopted and set at a shear rate of 0–120 s−1. The obtained flow curves were analyzed with the Bingham model because the thickened tailings showed a nearly linear rheological relationship, and this model was commonly utilized for paste characterization [43].

    4.   Results and discussion
    • During circulation, the underflow solid content was measured; the results are shown in Fig. 6. The circulation could reduce the underflow volume fraction by 0.8vol%–2.7vol%. The decrease in volume fraction mainly occurs at the initial period of the process. With the increase in time, the volume fraction tends to stabilize at a relatively low and stable level. It is inferred that with the increase in circulation height, the difference in volume fraction tends to be larger. The reason is that the solid fraction in a tall thickener during normal operation tends to be less uniform spatially; thus, switching to a uniform solid fraction during circulation could lead to a considerable change in a tall thickener, as compared with a shorter one in which nonuniformities are not large to start with. In addition, a large flow rate tends to contribute to a remarkable decrease in solid fraction instead of all converging to the same final state. A speculation is that in the pilot-scale thickener, the returned flow leads to a dramatic disturbance to the adjacent area, and the actual involved zone is larger than that of the circulation height, which is theoretically expressed as f(Q).

      Figure 6.  Changes in underflow volume fraction during circulation.

      The circulation results in a decrease in solid content with the increase in circulation height and flow rate and thus have a considerable influence on the rheological properties of underflow. The solid content and rheological properties of the underflow have been proposed to play an important role in avoiding rake failure and realizing normal thickener operations instead of overload shutdown [4445]. In varied circulation experiments, the underflows after circulation were sampled to measure their rheology. The shear stress–shear rate curves of the underflows in each test are shown in Fig. 7. With these curves, the yield stress and viscosity were obtained by fitting the Bingham model (Eq. (9)); the results are shown in Fig. 8.

      Figure 7.  Rheological properties of the underflow.

      Figure 8.  Yield stress and viscosity of the underflow: (a) relations to flow rate; (b) relations to circulation height.

      where $\tau $ is shear stress, Pa; ${\tau _0}$ is the yield stress, Pa; $\dot \gamma $ is the shear rate, s−1; ${\eta _{\rm{p}}}$ is plastic viscosity, Pa·s.

      The rheological properties of the suspension show a corresponding alleviation with the increase in height and flow rate. For yielding materials, the yield stress is considered a material property, indicating a transition between solid-like and liquid-like behavior; it is also defined as the minimum shear stress to initiate significant flow, i.e., the value of the shear stress at zero velocity gradient [46]. Results show that the yield stress decreases after circulation, corresponding to the change in solid content; that is, a large circulation height and a high flow rate result in a remarkable decrease in yield stress. By contrast, this process also leads to a decrease in plastic viscosity although without remarkable tendency along with circulation parameters (Fig. 8). In this case, the suspension is less likely to cause any rake failure.

      In the pilot-scale experiments, the circulation unit was effective in alleviating the tendency to cause excessive rake torque by reducing underflow solids fraction and rheology. Therefore, the changes in underflow volume fraction could be used for characterization of the performance of the circulation unit. The circulation height and flow rate could be optimized in accordance with actual needs, namely, the desired concentration that enables immediate restarting without causing thickener failure, as well as reduced power consumption and cost efficiency. A model would be helpful.

    • The results indicate that the change in the volume fraction of the underflow was not eminent in the circulation process even over a large height and flow rate. However, the yield stress of the underflow shows a substantial decrease. This result is in good accordance with the field thickening process wherein the rake torque is substantially reduced after circulation, thereby dramatically diminishing the possibility of rake failure. The correlation between the circulation parameters and the volume fraction of underflow is shown in Fig. 9.

      Figure 9.  Correlation between the volume fraction and circulation parameters.

      As indicated by Eq. (6), the change in volume fraction is in a nearly linear relationship with the circulation height and rate, which were obtained by fitting analysis on the basis of the experimental data. The results illustrated in Fig. 9 indicate that the decrease in the volume fraction of underflow could be expressed as follows:

      The performance of the circulation tends to be linearly related with its height and flow rate. In terms of the rheological properties of the underflow, the nonlinear fitting analysis of the yield stress and solid content was conducted by using the power law model (Eq. (8)). The results are shown in Fig. 10.

      Figure 10.  Effect of solid content on the underflow yield stress.

      The constants α and β (Eq. (8)) were experimentally determined as 358 × 103 Pa and 21, respectively. The fact that the constant β is large indicates that yield stress tends to be sensitive to solid content. In other words, the use of more kinds of tailings to test the performance of the circulation unit is preferable. In consideration of the poor repeatability in yield stress measurement, the dashed dotted lines were introduced to represent the 95% confidence interval for the fitted curve in Fig. 7; in other words, a 95% probability that the next measurement falls within the area between the two dotted lines exists [47].

      The fitting results reveal that the theoretical model is useful in describing the circulation performance. In practical application, the height f(Q) and the values k, α, and β could be obtained on the basis of fitting limited experimental results. This model could be used for an improved understanding of the circulation unit; moreover, it contributes to system design and optimization.

      In practical paste thickening, several factors could be considered for the design and operation of the circulation unit. These factors include the desired underflow concentration or yield stress value that would be maintained and energy consumption. In terms of coarse tailings that tend to cause rake failure, a large circulation height and pump rate are desirable for a considerable adjustment of underflow concentration and yield stress [48]. Generally, a discontinuous operation of the circulation unit is preferable and cost effective to avoid rake failure.

    5.   Conclusions
    • Circulation units are a requisite in paste thickeners to stabilize the underflow solid content and yield stress and thus avoid thickener failure, which may be caused by the long-time residence of tailings particles when the discharging is suspended. In this study, a mathematical model, which relates the circulation parameters with the resulted underflow concentration and yield stress, was proposed. In the thickening and circulation experiments conducted by using a self-designed thickening system, the circulation unit was proven to be effective in regulating underflow solid content and rheological properties. With the increase in circulation height and flow rate, a remarkable decrease in solid content to which the tendency of yield stress corresponds, occurred. The process also led to a decrease in plastic viscosity while showing a less substantial correlation with the circulation parameters. Through fitting analysis, this model described the circulation process and contributed to an improved understanding of the circulation operation. The high efficiency and improved performance of paste thickeners would benefit from further experiments and field tests on circulation units with different kinds of tailings.

    Acknowledgement
    • This work was financially supported by the National Natural Science Foundation of China (No. 51834001).

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