Optimization of drill bit replacement time in open-cast coal mines
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Abstract
To gain a competitive edge within the international and competitive setting of coal markets, coal producers must find new ways of reducing costs. Increasing bench drilling efficiency and performance in open-cast coal mines has the potential to generate savings. Specifically, monitoring, analyzing, and optimizing the drilling operation can reduce drilling costs. For example, determining the optimal drill bit replacement time will help to achieve the desirable penetration rate. This paper presents a life data analysis of drill bits to fit a statistical distribution using failure records. These results are then used to formulate a cost minimization problem to estimate the drill bit replacement time using the evolutionary algorithm. The effect of cost on the uncertainty associated with replacement time is assessed through Monte-Carlo simulation. The relationship between the total expected replacement cost and replacement time is also presented. A case study shows that the proposed approach can be used to assist with designing a drill bit replacement schedule and minimize costs in open-cast coal mines.
Keywords
Cost minimization Drilling operation Optimum replacement time Evolutionary algorithm Sensitivity analysis Monte Carlo simulationList of symbols
- α
Scale parameter (Weibull distribution)
- β
Shape parameter (Weibull distribution)
- C_{f}
Cost of failure replacement
- C_{p}
Cost of predicted replacement
- C_{t}
Total cost of expected replacement
- C_{tu}
Total cost of expected replacement per unit time
- EA
Evolutionary algorithm
- MTTF
Mean time to failure
- MWD
Measurement while drilling
- N
Natural numbers
- ROP
Rate of penetration
- R_{tu}
Probability of a predicted replacement
- S_{p}
Mean of the unshaded area
- t_{e}
Expected length of a bit usage
- t_{f}
Failure time
- t_{p}
Predicted length of a bit usage
1 Introduction
The mining industry made a significant progress on long-term mine planning in the previous decades (Kumral 2012). The next step is to develop tactical plans through addressing specific activities in mining cycle. Drilling is one of these activities. During open-cast coal mining, several benches must be created in both the overburden strata and the coal seam. A drilling operation is required where the overburden is hard. As a primary operation, drilling affects both the production and overall operating costs (Afeni 2009). The efficiency of the drilling operation depends primarily on energy consumption and on the drill bit life (Karpuz 2018) because a worn bit significantly decreases the rate of penetration (ROP). The driver of drill bit consumption is wear due to the interaction between the bit and the rock. Given that the bit cost is considered the most expensive part of a drilling operation, accounting for approximately 21% of total operating costs (Tail et al. 2010), it is vital to determine the ideal time to replace drill bits.
In current practice, a bit is replaced either when it drops into a drill hole during the operation, or the operator determines it is worn based on professional judgement (e.g., high vibration or significantly lower ROP can indicate a worn drill bit). In the latter case, the bit might be changed before its beneficial life has expired, which increases drilling costs unnecessarily. On the other hand, waiting to replace a bit until it is completely worn negatively affects the production rate. Although operator experience clearly plays an important role in drilling operations, a more objective approach to support bit replacement decisions is to monitor and analyze life datasets and use cost minimization methods (Hastings 2010).
The optimum replacement interval is the time period when the total operating cost is at its lowest (Jardine and Tsang 2013). Various researchers have developed strategies such as corrective and predictive maintenance (Tsang 1995) to determine optimal maintenance and replacement intervals (Verma et al. 2007). According to Tsang (1995) the high cost of maintenance activities is due to: (1) unscheduled events that stop ongoing operations and increase total downtime, thus delaying production targets and increasing labor costs; and (2) unexpected failures that may damage other parts of the system and result in health and safety problems. Critical to the development of a replacement policy is determining the optimum replacement interval to maximize the production rate, avoid unexpected failures, and minimize operation costs (Jardine and Tsang 2013).
Weibull analysis is a commonly used failure analysis technique because it has the ability to forecast with small samples numbers and the flexibility to represent most of the failure cases (i.e., it is capable of modeling both symmetrical and skewed datasets). It can also provide accurate statistical predictions about characteristics of the system (reliability, failure rate, hazard rate, and mean lifetime) and help decision-makers formulate reasonable predictions about the system (Jardine and Tsang 2013). Thus, Weibull analysis is extremely useful for planning maintenance schedules.
Most research on bit replacement strategies has focused on two factors: bit age (reliability) and ROP (production efficiency). For example, Godoy et al. (2018) modeled replacement strategy based on condition-based reliability. Hatherly et al. (2015) suggested using measurement while drilling (MWD) systems, which provides wellbore position, drill bit information and operating parameters, as well as real-time drilling information for rock mass characterization, blast design and optimization of fragmentation, to monitor bit wear. Li and Tso (1999) proposed a method to determine tool replacement time based on measurable signals such as cutting speed and feed rate. Tail et al. (2010) proposed a fixed reliability threshold to determine replacement time. Ghosh et al. (2016) and Karpuz (2018) used ROP as an indicator of drill bit replacement time, whereas (Bilgin et al. 2013) used rock condition as the indicator.
Unlike previous studies, optimal drill bit replacement time is calculated in this paper based on the minimization model of total expected replacement cost per unit time by the evolutionary algorithm (EA). The outcomes of the study are tested by Monte Carlo (MC) simulation with 100 randomly generated scenarios using Arena^{®} simulation software. In addition, a regression analysis is conducted to determine the relationship between the replacement time and the total cost of replacement. The originality of this paper resides in presenting a practical approach to determine the optimum drill bit replacement time based on the minimization of total expected replacement cost. Also, the relationship between replacement time and the related costs is quantified.
2 Research methods
The research was conducted in three stages: (1) life data (Weibull) analysis of drill bits, (2) cost minimization based on optimal replacement time, and (3) risk analysis based on the differences between costs of predicted replacement and failure replacement. Failure datasets were provided by MWD systems to analyze the behavior of drill bits. A Weibull model was fitted to drill bits, and the model parameters were calculated using ReliaSoft^{®} software. Finally, the optimization procedure was applied to determine the optimal replacement time with minimum total expected replacement cost per unit time based on the operating and maintenance cost.
2.1 Life data analysis (Weibull analysis)
In the case study, ModelRisk^{®} software was used to determine the Weibull distribution according to the Schwarz information, Akaike information, and Hannan-Quinn information criteria goodness-of-fit tests.
2.2 Cost minimization model
- (1)The cost of a failure replacement cannot be less than the cost of a predicted replacement.$$C_{f} > C_{p}$$(11)
- (2)The predicted length of a bit usage, the cost of a predicted replacement and the cost of a failure replacement are positive integer numbers (N).$$t_{p} ,C_{p} \,{\text{and}}\,C_{f} \in {\text{N}}$$(12)
- (3)The predicted length of a bit usage is larger than the mean time of the failure times.$$t_{p} > S_{p}$$(13)
- (4)The cost of a failure replacement is larger than the cost of a predicted replacement (Otherwise, drill bits can be used until the failure time.).$$C_{f} > C_{p}$$(14)
- (1)
Initial EA parameters (e.g., population size and mutation probabilities) are entered.
- (2)
Initial solutions corresponding to population size are created.
- (3)
Solutions are assessed relative to the fitness function.
- (4)
Using crossover and mutation operators and rank evaluation, previous solutions are perturbed, and the new solutions are generated and ordered.
- (5)
These solutions are assessed relative to the fitness function.
- (6)
The best solution is recorded.
- (7)
Steps 4–6 are repeated until EA converges.
2.3 Single-variable sensitivity analysis
Sensitivity analysis is used to quantify the effect of variation in input variable C_{f} in the model, which has a significant effect on the output and consequently, the cost. Single-variable sensitivity analysis is a technique to quantify the effect of variation of a single factor on the outcome, while keeping the other factors constant (Al-Chalabi et al. 2015).
It is common to use sensitivity analysis in mining research. Al-Chalabi et al. (2015) used sensitivity analysis to quantify the effect of the purchase price, operating cost, and maintenance cost of the drilling machine. de Werk et al. (2017) proposed a model to compare the parameters of two different material haulage systems by sensitivity analysis. Ozdemir and Kumral (2018b) applied sensitivity analysis to determine the impact of variations of explosive price, the unit cost of equipment, and electricity price on the total mining operating cost. Yüksel et al. (2017) performed sensitivity analysis to prevent long-range spurious correlations for block size localization in open-cast coal mines.
2.4 Monte Carlo simulation (MC)
MC generates random realizations to find an appropriate solution to a stochastic problem (Shonkwiler and Mendivil 2009). Sembakutti et al. (2017) proposed an approach to model fleet availability in open-pit mines by MC. de Werk et al. (2017) applied MC to assess the uncertainty design parameters of material handling systems in open-pit mines. Ozdemir and Kumral (2018a) generated random variables from a probability distribution with MC for uncertain variables of a material handling system (e.g., loading time, hauling time, and payload).
3 Case study
The results show no trend in the failure data; therefore, the renewal process was conducted, and the 2-parameter Weibull distribution was determined, using α = 3.8 and β = 53.3. These parameters can be different based on the rock condition. For the hard rock formations, because of the shorter bit life, the parameters can be smaller.
Optimum variables
Variable | Value |
---|---|
C_{p} (C$) | 10,000 |
C_{f} (C$) | 15,000 |
R _{ tu} | 0.43 |
1 − R_{tu} | 0.57 |
S_{p} (h) | 38.00 |
t_{p} (h) | 51.00 |
C_{tu} (C$/h) | 293.77 |
From Fig. 5, it is evident that there is a slight difference between changing the bit in 47 h and 51 h in terms of the cost of operation per unit time ($0.50). However, changing the bit before the end of beneficial life incurs a substantial cost to the company, approximately 8% less operation time per bit. In other words, drill bit consumption increases by approximately 14 bits per machine per year, a cost of around $70,000. On the other hand, if the bit is changed 4 h after t_{p}, the cost increases $7.00 per unit time and the probability of failure increases by 70%.
Results of sensitivity analysis
Variation of C_{f} (%) | C_{tu} ($) | t_{p} (h) |
---|---|---|
0 | 293.77 | 51 |
10 | 310.35 | 46 |
20 | 326.00 | 45 |
30 | 341.14 | 44 |
40 | 353.60 | 40 |
Predicted drill bit replacement times and costs based on MC
Predicted replacement time (h) (t_{p}) | Number of predicted replacements | Number of failure replacements | Total number of bits used | Total replacement cost (C$) (replacement cost + bit cost) (C_{t}) |
---|---|---|---|---|
43 | 12 | 5 | 17 | 280,000 |
47 | 11 | 5 | 16 | 265,000 |
51 | 9 | 5 | 14 | 235,000 |
55 | 6 | 9 | 15 | 270,000 |
59 | 4 | 11 | 15 | 280,000 |
63 | 4 | 13 | 17 | 320,000 |
The R-square of the proposed quadratic model is 0.89, showing that the fitted curve is close to the model.
4 Conclusion
This paper proposed a practical approach through a cost minimization model to determine optimum replacement time for drill bits based on replacement costs. The approach presented herein is based on failure data of the drill bits and the maintenance cost of the replacements. First, the Weibull life data analysis was applied to time-to-failure data to obtain parameters of the model. Replacement time was formulated as a minimization problem. In a case study, the EA was used to determine the optimum time to change the drill bits for an open-cast mining operation. Model results show that increasing the operating time of drill bits by 8% can make a considerable impact on the total replacement cost of a drilling operation. The proposed approach can be used to facilitate decision-making for replacement scheduling.
In addition, a sensitivity analysis was conducted to quantify the relative importance of the cost of a failure replacement. Results indicate that increasing the cost of a failure replacement negatively affects the total cost of expected replacements per unit time and the length of the predicted cycle (the optimum replacement time). In other words, when the cost of a failure replacement increases, the optimum interval time to use the drill bits decreases. Thus, the proposed approach can also be used to assess the risk of the replacement decision.
MC simulation was implemented to determine variation of total replacement cost. The total replacement cost can be reduced by approximately 11% by using a 51-h replacement time relative to a 47-h replacement time. Hence, the simulation results support the consistency of the proposed approach.
Lastly, the relationship between drill bit replacement time and the total drill bit replacement cost was formulated by a quadratic regression equation using the results of the MC simulation. Using this equation, the total replacement cost can be calculated when the drill bit replacement time is chosen. It is important to note that the results obtained from the simulation and the regression are site-specific. Different results can be obtained from different rock formations. The model must be implemented to the different cases in order to have an accurate result. For harder rock formations the optimum bit usage length can be shorter.
In future studies, the variables that affect the maintenance cost will be investigated in detail. The constants of the objective function, the cost of a failure replacement, and the cost of a predicted replacement will be modeled as the functions of maintenance cost elements, and the total cost of the replacement will be formulated with these cost elements.
Notes
Acknowledgements
The authors gratefully thank the Natural Sciences and Engineering Research Council of Canada (NSERC) (ID: 236482) for supporting this research.
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