A novel semiautogenous mill liner wear kinetics model.

Karamoozian, Mohammad ; Shafaei, Seyed Ziaedin ; Kakaie, Reza 等

Introduction

The application of large AG/SAG mills in the mineral industry has been increasing owing to a significant reduction in capital and operating costs and promotion in the plants throughputs. The availability of these mills has great influence on the operation economics. One of the major reasons of mill pauses is the time required to change worn or broken liners. This factor not only reduces the production rate but also imposes a high liner and replacement costs. Liner wear influences the mill load behavior, which consecutively alters the mill performance. The awareness of the liner wear rate and profile facilitate the estimation of the liner life and also provides useful information on how to reduce any defects by modifying the original design. Maximizing the liner life has been one of the main objectives of both manufacturers and mill operators. There is no comprehensive solution and operating conditions to determine the proper measures. The change in the ore hardness and other operating parameters can impose such a significant impact on the liner life that all measures taken on the liner to make longer its life may not lead to productive results. It is common to monitor the wear profile of the liners and make modification based on the final profile to arrive at a smooth profile when the liners are changed.

The various approaches which have been employed to increase the liner life are as follows: increasing lifter height[1,2,3], changing lifter release angle[4], decreasing the number of liners[5], increasing charge level[6], decreasing mill speed[7] and using high-low liner configuration[8]. Welding of cracked liners in specific situations has also been practiced to extent the liner life. [5,7].

The common method to determine the wear profile has been two dimensional and the weight estimation has been performed assuming a uniform wear profile [9]. In this study, in order to determine the wear rate, the kinetics wear model of SAG mill liners is proposed based on frequent profile measurements. This not only enabled the estimation of the liner change out time but also provided the evolution of liner profile during operation. The common criterion of liner change out time, which is based on the height of the lifter, was examined. This research project was initiated to develop a method to model the liner wear at any given operating time with the aim of increasing the mean liner life time.

Wear rate determination methods

The common method

The basic idea is to assume a uniform wear profile for a liner and measure the profile at one cross section. After placing the measuring device, which usually consists of needles, on the liner the length of the needles are marked on the paper. The cross section is obtained by converting the marks on the paper to the numbers showing the length of each needle. Then the wear rate is calculated by comparing the profiles at different time intervals with the original profile [1].

Kinetics model of liner wear

Nowadays, increasingly detailed and complete predictions of mill behavior, including high resolution predictions of liner stresses and wear rates and detailed collision energy spectra are made possible with DEM modeling [10]. But in this study, kinetics wear model is used to describe the liner characterizations because it is easier to be used and also the model conditions are more similar to the real data.

To study the kinetics of liner wear it was found that a zero order kinetics model could well be used to describe the data. The relationship is in the form of:

[dL.sub.T]/dt = -k (1)

where [L.sub.T] is the liner thickness, and k is the rate constant. Upon integration and rearranging:

[L.sub.T] = [L.sub.T0] - kt (2)

where [L.sub.T0] is the initial liner thickness.

To determine the rate constant of the zero order kinetics model, the normalized liner thickness (i.e., liner thickness at time t, that is measured inside the mill during the mill shut-down periods, divided by the initial liner thickness) versus operating time was drawn in a log-normal graph. This model can calculate the liner thickness at any given time. The rate constant is related to liner type, liner shape, wet or dry grinding, charge, ball percent, solid percent, mill speed, and etc.

Case Study

The Sarcheshmeh concentration plant has a 9.75 x 4.88 m constant speed (10.5 rpm) SAG mill with two 5500 hp motors, which could rotate in two directions. In the grinding circuit, a 6.7 x 9.9 m ball mill with two 5500 hp motors works in a closed circuit with 66 cm diameter cyclones. The feed to the SAG mill is under 17.5 cm, which is the product of a gyratory crusher. The discharge of the SAG mill goes to a vibrating screen with the openings of 5 mm. The oversize material is recycled to the SAG mill and the undersize is combined with the ball mill discharge and is sent to the cyclones. The cyclone underflow is fed to the ball mill and the overflow with [P.sub.80] of 90 [micro]m is directed to the flotation circuit.

The SAG mill inside shell has been covered with two series each consisting of 60 rail type liners. The liners are cast chrome-molybdenum steel with a Brinnell hardness between 325 and 375. The lifter height is 152 mm and they have to be changed based on the manufacturer's recommendation when two-third of the lifter height worn away. The main features of the SAG mill liners are shown in Table 1.

To validate the zero order kinetics model, the normalized liner thickness (i.e., thickness at time t divided by the initial liner thickness) versus operating time was drawn in a log-normal graph (fig.1). The model fits the data very well ([R.sup.2] = 0.997) and the rate constant found to be equal to 1 x [10.sup.-4][h.sup.-1].

This model can calculate the liner thickness at any given time. For example, after 3500h of operation the liner thickness decreases from the original weight of 152 mm to 100 mm.

Validation

The liner wear kinetics model is validated with mass balance method that is proposed by Apelt [11]. He expressed that the mill liner wear rate, can determined from the change-out frequency and the relative change in shell lining thickness at change-out time. Based on typical plant experience, the change-out frequency is approximately 4000 h, and the change-out time, based on the manufacturer's recommendation is when two-third of the lifter height worn away i.e.,

Wear rate=[L.sub.sm] x [[rho].sub.liner] x nl x 1/3lbw/1000 x (lt-slt)/1000 + [pi] x [L.sub.sm] x [[rho].sub.liner] x [D.sub.sm0] slt/1000/4000 (3)

where [[rho].sub.liner] is the liner density (t/[m.sup.3]), nl is the number of lifter bars, lbw is the lifter bar width (mm), lt is the lifter bar thickness (height) (mm), slt is the shell liner thickness (height) (mm) and [L.sub.sm] is the SAG mill shell length (m). In equation (3),The first term is the weight of portion of lifter bars that protrude above the shell lining and the second term represents the weight of an annular piece of shell lining of thickness slt, defined by the shell inside diameter, [D.sub.sm0] (m).

Assuming that wear is uniform throughout the shell liner of the mill, the wear thickness, wt (the amount of lining component that has been worn away) (mm) can be determined by equation (4):

(First shell lining weight) - Wear rate x t - (Worn shell lining weight) = 0 (4)

"worn shell lining weight" should express in terms of wear thickness, wt, by the substitution of (slt - wt) for slt in lining weight equations (equation (5)) :

Worn shell lining weight = [L.sub.sm] x [rho]liner x nl x lbw/1000 x (lt-slt- wt)/1000 + [pi] x [L.sub.sm] x [[rho].sub.liner] x [D.sub.sm0] slt-wt/1000 (5)

then wt can be determined by solving the equation (4).

Then the predicted values of liner thickness are calculated upon different operational time. The results showed a very good correlation of the kinetics model, measured data and the wear thickness model (Fig.(1)) .

[FIGURE 1 OMITTED]

To validate the order of the kinetics model, five different kinetics orders are checked which are as follows:

Model 1(kinetics model of order 0): [dL.sub.t]/dt=-[kL.sup.0.sub.T0] (6)

Model 2 (kinetics model of order 1): [dL.sub.t]/dt=-[kL.sup.1.sub.T0] (7)

Model 3 (kinetics model of order 2): [dL.sub.t]/dt=-[kL.sup.2.sub.T0] (8)

Model 4 (kinetics model of order 0.5): [dL.sub.t]/dt=-[kL.sup.0.5.sub.T0] (9)

Model 5 (kinetics model of order 1.5): [dL.sub.t]/dt=-[kL.sup.1.5.sub.T0] (10)

The results of different kinetics models are presented in figure 2. The results show that zero order of kinetics model has the best correlation to measured data.

[FIGURE 2 OMITTED]

Conclusions

1. The SAG mill liner wear is subjected to the zero order kinetics model.

2. The comparison of the measured and modeled data of liner thickness, it was found that the proposed model could get a good fit to measured data.

3. The new model was proposed to make possible the SAG mill liner wear prediction at any given operating time.

4. Using this model, the liner change out time can be determined easily.

Acknowledgements

The authors would like to thank National Iranian Copper Industries Company (N.I.C.I.Co.) for supporting this research. Special appreciation is also extended to the operating, maintenance, metallurgy and R&D personnel for their continued help.

References

[1] Orford, I., Larsen, C., Cooper, M., Renaud, M., Strah, L., 2003. Brunswick Mine SAG mill liner design and wear. In: 35th Canadian Mineral Processors Operators Conference, January 21-23, Ottawa, Canada, pp. 85-100.

[2] Bustos, E.B., Mills, F.C., and Cuarda, O.T., 1996. Semiautogenous grinding and liner designs at the Codelco Chile "EL TENIENTE Division". In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. Vancouver, October 6-9, pp. 1017-1033.

[3] Parks, J.L., 1990. Liner design, materials and operating practices for large primary mills. CIM Bulletin 83 (943), 84-89.

[4] Bird, S., Lamb, A.E., Lamb, W., Partridge, D.W., 2001. Evolution of sag mill shell liner design at Kennecott Utah copper concentrator, SAG 2001. In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. University of British Columbia, Vancouver, BC, Canada, September 30-October 3, pp. 256-269.

[5] Miranda, D.G., Bassaure, F.T., Marsden, J.O., 1996. Evolution of liners for a 360 x 150 (EGL) SAG mill at Candelaria. In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. Vancouver, October 6-9, pp. 857-880.

[6] Sherman, M., Rajamani, R., 1999. The effect of lifter design on Alumbrera's SAG mill performance: design expectations and optimization. In: 31st Annual CMP Meeting, Ottawa, Ontario, pp. 255-266.

[7] Kendrick, M.J., Marsden, J.O., 2001. Candelaria post expansion evolution of SAG mill liner design and milling performance, 1998-2001, SAG 2001. In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. University of British Columbia, Vancouver, BC, Canada, September 30-October 3, pp. 270-287.

[8] Meekel, W., Adams, A., Hanna, K., 2001. Mill liner development at highland valley copper, SAG 2001. In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. University of British Columbia, Vancouver, BC, Canada, September 30-October 3, pp. 24-240.

[9] Meekel, W., Adams, A., Clark, J., Mitchell, J., 1996. Primary mill liner development at highland valley copper. In: International Autogenous and Semiautogenous Grinding Technology, vol. 3. Vancouver, October 6-9, pp. 913-933.

[10] Cleary, P.W., 2001, Recent advances in DEM modeling of tumbling mills, Minerals Engineering, Vol. 14. No. 10, pp. 1295-1319.

[11] Apelt, T.A., Asprey, S.P., Thornhill, N.F., 2002. Inferential measurement of SAG mill parameters II: state estimation, Minerals Engineering 14 (6), 575-591.

Mohammad Karamoozian (1), Seyed Ziaedin Shafaei (1), Reza Kakaie (1), Mohammad Noaparast (2) and Sedigheh Zeidabadi (3)

Mining, Petroleum and Geophysics Faculty, Shahrood University of Technology, Shahrood, Iran Email: mohammad_karamoozian@yahoo.com Faculty of Mining Engineering, University of Tehran, Tehran, Iran. R & D Center, Sarcheshmeh Copper complex, Rafsanjan, Kerman, Iran

Table 1: Some characteristics of Sarcheshmeh SAG mill liners

 Volume    Weight   Length     Cross        No. of         No. of
[m.sup.3]    kg       mm      section     lifters in    lifters along
                             [cm.sup.2]   each series    mill length

 0.1407     1130     2084       672           60             2

Table 2: Sarcheshmeh Mill Lining Specifications

                     item                        value

liner density [[rho].sub.liner], (t/[m.sup.3])    8.03
r liner
number of lifter bars, nl                          60
lifter bar width, lbw (mm)                        192
lifter bar thickness(height), lt (mm)             228
shell liner thickness (height), slt (mm)           76
SAG mill shell length, Lsm (m)                    4.42
shell inside diameter, Dsm0 (m)                   9.5

Table 3: Mill Liner Model Results

item                               value

Wear rate, (t/hr)                  0.0253
Wear thickness, wt (mm/hr)         0.0172
= Thickness worn away each hour