How to Account for Operating Condition Variability When Predicting Liner Operating Life with DEM – A Case Study Jochen Franke* Outotec Pty Ltd, West Perth, Australia, R&D Manager - PCMP, +61 8 9211 2200,
[email protected] Paul W. Cleary CSIRO Mathematical and Information Sciences, Clayton South, Australia, Chief Research Scientist, +61 3 9545-8005,
[email protected] Matthew D. Sinnott, CSIRO Mathematical and Information Sciences, Clayton South, Australia, +61 3 9545-8034,
[email protected]
ABSTRACT Wear prediction is important in the development and optimisation of liners and for helping to manage reline strategies. DEM is able to predict wear and profile evolution of liners over the life cycle for specific sets of conditions. However, in real operations conditions often vary - usually in ways that are not known in advance, which limits the ability to use such model predictions in managing associated wear. In this study, we use a specific case to explore issues around the variability of wear caused by different operating conditions within the applicable range for the mill, and consider how these can be included in a modelling frame work in order to assist with mill liner management. *Corresponding author
KEY WORDS DEM; wear liner prediction; operating condition variability; liner life
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INTRODUCTION One of the key drivers for efficient grinding mill operation is the implementation of an efficient reline regime for installed sacrificial liners. This prevents costly and disruptive reactive maintenance requirements that otherwise occur in industry practice. Scheduling of relines is based on the expected life cycle of liner segments installed, which typically varies between segment types, depending on their location inside the mill and associated intensity of exposure to abrasive charge contact corresponding with according wear rates. Other factors include the design of new liners such as plate and lifter thickness, effective lift, stepped lifter bars, lifter bar spacing, and many other geometry and dimensional considerations. Liner life expectancy for each segment type can vary from cycle to cycle due to changes in operating conditions that are caused by a range of site specific ore body, mining and feed preparation variables as well as human operator subjectivity, liner material or manufacturing flaws, or even commercial constraints. A suitable reline regime may be based on production considerations as described by Toor et al. (2013), on maintenance preferences or priorities, or a balance of both. Whichever is the main concern, the following methods for quantifying the next required reline are current industry practice : 1.
Dead reckoning, empirical estimate – the most unsafe and unreliable option
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Manual liner measurements using rudimentary tools such as nail gauges, nails, or tape measures to track and extrapolate reline dates – an unreliable and therefore unsafe option
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Manual liner measurement using ultrasonic gauges to track and extrapolate reline dates – an option that can be reliable, but requires diligent instrument calibration, skilled confined space operation, and only works on specific liner materials
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MillMapper® measurement – the industry standard for remote, universal and reliable wear tracking and reline prediction in digital form
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DEM wear prediction based on physical definition of mill operation in digital form – an attractive but yet to be universally proven technique
MillMapper® laser scanning based data can be used to rapidly create highly accurate digital models of the internal working surfaces of a SAG mill. This data can also form the basis for extracting other condition monitoring information such as an accurate and statistically representative ball size distribution, grate open area and quantified charge volume. Discrete Element Method (DEM) modelling has been used for many industrial applications, including grinding mills, in order to gain insight into actual operational behaviour. This can provide a decision making tool for process improvements when other tools such as available on- or offline production monitoring systems cannot provide immediate or holistic answers. DEM is also capable of liner wear prediction which is of significant interest from a “what if” liner design, or from a mill control system perspective for example. For such predictions to be representative of real operation, the DEM algorithm requires predicted and representative knowledge of all relevant parameters affecting liner wear over a whole life cycle, such as changes in feed characteristics, operator intervention variability regarding mill fill, ball addition rate or mill speed, variability in reline strategies of individual segment types, and more. Since these parameters cannot be reliably or accurately sourced for the great majority of industrial mill operations and typically they are not known in advance, it is necessary to calibrate or train the mill liner wear prediction algorithm with liner wear measurement data that inherently accounts for all relevant parameter changes. In this paper, a specific industrial MillMapper® data set is used as input into CSIRO’s threedimensional DEM solver in order to explore approaches to taking account of operating condition variability and how this can be combined with a priori DEM simulation to provide usable information that can be of practical assistance to mill operators making mill reline decisions.
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DEM WEAR PREDICTION PURPOSE The primary focus of this paper is on the issue of mill liner wear prediction for maintenance purposes which is of highest priority for site personnel. There is however a secondary and arguably equally important purpose for DEM wear prediction that is unrelated to direct operational control. Since DEM wear prediction can theoretically provide output without measurement input, it can be used to explore the efficiency of hypothetical new liner designs. As indicated earlier, wear prediction for maintenance purposes requires knowledge of future operating parameters that often cannot be sourced at all or determined to a sufficient degree of accuracy. Such accuracy may however not be required to determine whether a particular liner design would likely achieve a better or worse set of production parameters when compared to a current design or to other alternative design options. The most relevant information in this instance is the overall typical performance relative to those of other designs, not so much the representative reflection of actual behaviour at a particular point on the production calendar. Aside from simulation, the only alternative and to date most commonly used method to achieve this is to evaluate new liner design performance by trial and error – in other words to design, manufacture, supply, install, track, and then compare it to the performance of the original design. Naturally this process has many disadvantages including very long lead times to obtain results of at least many months if not years, the high cost of trial liner manufacture, and the significant risk of inconclusive results. Liner performance comparison can only be valid if operating conditions are ideally the same or at least similar during the life cycle of the different installed liner designs, which can rarely be achieved in practice. Some sites have attempted to eliminate this need and to minimise liner trial costs by only installing a limited number of individual segments of the new design with the remaining segments installed featuring the original design. Whilst this approach is suitable to highlight performance differences of varying liner materials if no major design changes have been implemented, it is not suitable to establish representative behaviour of a full set of truly different liner designs respectively. Another major disadvantage of improving liner designs through the trial and error method is that only one new option can be assessed at a time. Other variations can only be considered in iterative sequence which may mean that a truly optimised design can take years to achieve or could even take the end point of identifying a best performing liner assembly beyond the remaining mine life and therefore render the whole process inadequate. DEM liner performance evaluation on the other hand can assess as many design variables as desired in parallel. The only limitation is computing power for complex models which in the context of time requirements of the trial and error method is negligible.
DEM SOLVER OVERVIEW DEM simulation involves following the motion of every particle in the flow and modelling each collision between combinations of particles and between particles and their environment such as the liner of a mill. The general DEM methodology and its variants are well established and are described in review articles by Barker (1994), Campbell (1990) and Walton (1994). The implementation used here is described in more detail in Cleary (1998, 2004, 2009). Briefly, the particles are allowed to overlap and the amount of overlap x, and normal vn and tangential vt relative velocities determine the collisional forces via a contact force law. A linear springdashpot model is used for particle-particle and particle-boundary collisional force. Other contact models could be used (see Thornton et al., 2011, 2013, for detailed expositions of all such contact models for elastic and inelastic systems). The normal force:
Fn knx Cnvn
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(1)
consists of a linear spring to provide the repulsive force and a dashpot to dissipate a specified proportion of the relative kinetic energy. The maximum overlap between particles is determined by the stiffness kn of the spring in the normal direction. Typically, average overlaps of 0.1-0.5% are desirable, requiring spring constants of the order of 106 N/m for mills modelled in three dimensions. The normal damping coefficient Cn is chosen to give the required coefficient of restitution (defined as the ratio of the post-collisional to pre-collisional normal component of the relative velocity), and is given in Thornton et al. (2013). The tangential force is given by:
Ft = min mFn , å kt vtd t + Ct vt
{
}
,
(2)
where the vector force Ft and velocity vt are defined in the plane tangent to the surface at the contact point. The integral term represents an incremental spring that stores energy from the relative tangential motion and models the elastic tangential deformation of the contacting surfaces, while the dashpot dissipates energy from the tangential motion and models the tangential plastic deformation of the contact. The total tangential force Ft is limited by the Coulomb frictional limit Fn,, at which point the surface contact shears and the particles begin to slide over each other. Industrial applications place heavy demands on the geometrical capabilities of DEM codes and can affect computational performance. Boundary objects are defined here, for three-dimensions, by triangular finite-element surface meshes. These meshes can be produced using any reasonable mesh generator from solid models generated in suitable CAD packages. This provides enormous flexibility in specifying three-dimensional environments with which the particles interact. The particles are represented as either spheres or super-quadrics: m
m
m
x y z 1 a b c
(3)
The ratios of the semi-major axes b/a and c/a are the aspect ratios of the particles and the superquadric power m determines the shape of the particle. For m =2 a spherical particle is obtained. As m increases, the shape becomes progressively more cubic with the corners become sharper and the particle more blocky. By m = 10, the particle shape is essentially a cube (for aspect ratios 1). This is a very flexible class of shapes, which varies continuously (m is not restricted to integer values). This allows plausible shape distributions to be represented and the shape can be made to change dynamically during simulation (for example with abrasion as measured by the shear energy dissipation on the particle). Super-quadric particles are a good representation of conditioned (rounded) ROM ore, but for convenience in this wear modelling we use spherical particles. The discrete element algorithm has three essential parts: 1.
A search grid is used to periodically build a near-neighbour interaction list that contains all the particle pairs that are likely to experience a collision in the short term. Using only particle pairs in this list reduces the contact detection calculation to an O(N) operation, where N is the total number of particles. Industrial simulations with up to 100 million particles are now possible in reasonable times on current compute servers.
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For pairs of particles or particles and objects in the near-neighbour list, the closest distance between them is calculated in order to determine if they are in contact. The contact forces between each pair of interacting particles and/or boundary objects are then evaluated in their local reference frame using the spring-dashpot model and then transformed into the simulation frame of reference.
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All the forces and torques on the interacting particles and objects are summed and the resulting equations of motion (for position, velocity, orientation and spin) are integrated. Time integration is performed using a second-order predictor-corrector scheme and typically
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uses between 15 and 25 time steps to integrate accurately each collision. This leads to fairly small time steps (typically 10-5 to 10-6 s depending on the controlling length and time).
The nature of the quantitative predictions that one wants to make using the extensive state data available in DEM simulations depends very much on the application and the questions one is seeking to answer. For industrial applications this information frequently falls into one of these categories:
Boundary stresses (for mechanical design and fatigue prediction).
Wear rates and distributions (for estimating the life span of equipment and wear components). Liner geometry can be evolved in response to wear predictions allowing life cycle predictions to be made (Cleary et al. 2010).
Accretion rates (for predicting accretion induced blockage, changes in open area of screens).
Collisional force distributions, collision frequencies, energy absorption spectra (for understanding breakage and agglomeration).
Power consumption and torques (for equipment design).
Flow rates and flow statistics (for summarising characteristics of complex flows)
Sampling statistics (to assess the accuracy of various sampling processes).
Mixing and segregation rates (to assess the progress of intended mixing and de-mixing processes and to understand the degree of segregation and its effects on other processes where segregation and/or mixing are not intended).
Residence time distributions (to assess the range of times that particles are exposed to various environments within a process, for example in granulation and in comminution)
Axial transport rates (to assess the axial flow along cylinders (rotating and stationary) that are commonly used).
For more details on the simulation method and on the data analysis methods see Cleary (1998, 2004, 2009).
CASE STUDY The main proposition of this paper is that it is highly unlikely for the vast majority of industry cases to have the opportunity to establish representative future operating parameters for a liner life cycle that are representative enough to ensure just-in-time relining through DEM wear prediction based on a single idealised set of input conditions. The clear aim is to achieve the pre-determined criteria of optimum production performance and durability to an acceptable tolerance, subject to the operating variability that will inevitably arise. This requires wear prediction and its associated reline forecast to establish a sufficiently conservative reline tonnage without risking liner failure, particularly due to accelerated wear rates towards the end of liner life, which is a common phenomenon. Overestimation of remaining life, sometimes by only a few days, can lead to catastrophic liner failure affecting the integrity of the mill itself. Such cases have occurred and are an ever present danger. Underestimating remaining life leads to inefficiencies that can carry significant overheads such as production loss, lower mill availability, maintenance bottlenecking, and higher liner and labour costs. The stringent requirements on reline forecasting and therefore wear prediction for maintenance purposes mean that utilising the DEM approach can only be successful if all parameters and their variations over time that have a notable effect on wear rates are somehow included in the modelling. The critical challenge is that the magnitude of influence by each parameter and the influence of variability of each on wear behaviour is not yet well understood and cannot be known fully in advance. This presents quite a complex problem proposition.
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The following case study illustrates the influence that selected parameters known to affect liner wear can have on DEM wear prediction. The degree of influence that parameter variability can have is also assessed and highlighted. Care was taken to utilise actual industrial values so as to provide a realistic insight.
Case Study Data Set The case study is based on industrial data for a 11.4m (38’) diameter by 7.6m long 18MW Autogenous Grinding (AG) mill lined with grates of nominal 20 mm aperture and pebble ports of nominal 70 mm aperture. The mill liner is shown in Figure 1. The following input parameters were sourced from nine MillMapper® surveys over a life cycle of close to one year :
Highly detailed liner geometry at nine wear stages from new to completely worn
Charge volume as a % filling of mill volume at each applicable liner wear stage
Mill volume at each applicable liner wear stage
Estimate of particle size distribution (PSD) present in the mill
Particle size distribution was extracted from MillMapper® three-dimensional laser scan data of the visible charge surface (see Figure 2). Sub-surface layers may vary from these characteristics, likely trending to a smaller distribution due to the percolating effect during the process of stopping the mill. Nevertheless, lacking more accurate traditional sizing campaign data achievable through careful sampling and subsequent sieving, this was the best available information and is superior to any manual spot check, let alone dead reckoning. It also represents the particle size distribution actually present in the mill as opposed to feed or product size distribution traditionally collected through conventional sampling and is therefore more applicable to assessing any in-mill behaviour. Terrestrial Laser Scan (TLS) data in use by MillMapper® does not lend itself to reliably measure fines below a size of approximately twenty millimetres because achievable data resolution, point precision, and inter-particle obstructions prevent that. In order to obtain an estimate of fine particle content in the mill charge, the ratio of scan points for coarse and fine particles was used to calculate associated fill percentages. All fine particles were defined as
