Modeling Analysis of the Influence of Mineral Price on the Boundary Grade of Polymetallic Deposits

China is a country rich in mineral resources. It has a complete range of products, but its per capita possession is small. The deposits are mostly associated with mineral deposits, and there are many poor ore, less rich ore, and complicated mining conditions [1]. The development and utilization of mineral resources is determined by internal factors and external environment: internal factors include deposit conditions, mineral composition, grade distribution, geological reserves, etc.; external environment includes market supply and demand, national policies, domestic and international economic environment, mining technology Factors such as level, advanced equipment level, and management level.
In recent years, the price fluctuations of mineral products have been turbulent, which has a great impact on the production management of mining enterprises.
The geological reserves of a particular deposit are basically determined. According to the relevant literature, the current reserves of the deposit are estimated by the Kriging method and its variants [2]. Closely related to reserves and taste, with Hu, who is the multi-dimensional probability distribution model between multi-grade distribution of metal deposits and reserves [3]. China's industrial-grade index system is used in cutoff grade and industrial grade indicators [4], commodity prices in different periods of socio-economic development subject to change, according to the data from the [5-6], in 2011 China's iron ore price from 1200 yuan / t gradually reduced to 728 yuan / t in August 2014, the decline in the price of mineral products directly reduced the company's income, or even a loss, mining companies can only reduce costs through various technical optimization methods to survive. The low-grade gold Purple optimization, 0.2g / t ore body, reducing the average grade of 71 43.8% 49.5% increase reserves [7] by reducing industrial grade; breakeven analysis using Ta-Nb ore Ichun Determine the break-even grade [8]; Canada's KiddCreek copper - zinc - silver mine uses a mixed integer programming model to optimize the design of the stope to obtain maximum benefits [9].
Analysis of the relationship between cost, price and grade indicators is necessary for the current mining industry to enter a period of turbulent downturn. The price change forces the mine to adjust accordingly, that is, adjust the grade indicators, re-define the size of the ore body; improve the production process, and even Change mining methods and reduce costs. For the first method, most scholars adjust the grade index through the break-even analysis method [10]. However, these methods often have limitations such as not considering the time value of funds or the variability of not considering the cost. Open pit mining process [11], to improve the production process technology.

Based on this, this paper will comprehensively consider the mining, selection and smelting process of mining enterprises, establish a mathematical model based on the economic analysis method of profit, and deeply analyze the impact of mineral product price changes on marginal grades, mining methods, corporate profitability and so on. Provide decision makers with a basis for decision making.
1 Derivation of profit-based analysis model
1.1 Basic assumptions
In order to improve the applicability, it is assumed that the deposit is a common and associated deposit of two metals, and the content ratio is relatively fixed. In the interpretation of the ore body, the ore body is generally delineated according to the grade of the main metal, and other metals are treated as an accessory product obtained by recovering the main metal. The ore bodies delineated by different boundary grades are very different, especially for multi-metal associated and symbiotic deposits, and the delineation of industrial reserves is more complicated [12]. The determination of the cut-off grade is also related to the current technical level. Most mines, especially those that have been mined for many years, are basically difficult to re-arrange the ore bodies, so the industrial reserves of each deposit in this paper are assumed to be constant.

The economic break-even analysis method is adopted, which fully considers the cost and the selling price, and derives the calculation of the profit function model, so as to analyze the impact of the cut-off grade and product price on the profit during break-even.
1.2 Determine the total amount of metal
After adopting a mining method, the loss rate ρ and the depletion rate γ can be determined, and the total amount of ore produced and the parameters of the mining and metallurgy can be used to calculate the output of the final smelted metal product:

Where M is the total amount of metal product finally smelted; T is the total amount of ore mined; gav is the average ore grade of ore, gav1/gav2=k in the same deposit, which is constant; rp is the recovery rate of ore dressing ; rs For smelting recovery rate.
Considering the depletion of mining losses, industrial reserves Q is not the total amount of ore mined, the relationship is:

Where ρ is the loss rate; γ is the depletion rate.
1.3 Determine total cost and sales revenue
Under the established industrial reserves and mining methods, the total cost of mining and smelting is:

Where, Cm is the mining cost per ton of mine, that is, the sum of all the costs of producing 1t of raw ore to the yard; Cp is the cost of ore dressing, which is the sum of all costs of processing 1t raw ore; Cs is the cost of ton metal smelting, ie Summarize the sum of all costs for 1t metal products.
The sales revenue S of the final metal product obtained from smelting is:

In the formula, P1 and P2 are the selling prices of the main metal and by-product metals of the final product, yuan/t.
1.4 Profit model
Through the above derivation, the final profit function G can be obtained, ie

According to formula (5), the market price is known. Under the established mining method, beneficiation and smelting process, only the unknown gav, and the formula (5) is equal to zero, can find the boundary grade when the break-even of the price changes.
2 case application
2.1 Corporate Background
Jinchuan Group Co., Ltd. is a large state-owned company, a joint non-ferrous metallurgical and chemical enterprise engaged in mining, selection and smelting. Main production of nickel, copper, cobalt, platinum, noble metals, non-ferrous metal rolling processing products, chemical products, chemicals and other non-ferrous metals. The company has formed an annual production capacity of 150,000 tons of nickel, 400,000 tons of copper, 10,000 tons of cobalt, 3500kg of platinum group metals, 8t of gold, 150t of silver, 50t of selenium and 2.5 million tons of inorganic chemicals. There are 3 production mines in Longshou Mine, No. 2 Mining Area and No. 3 Mining Area. Based on the engineering background of the three mining areas, this paper defines the ore body according to the boundary grade of 0.35% nickel. The industrial reserves are 32.78 million tons, the nickel comprehensive grade is 0.66%, and the average copper grade is 0.44%. Currently, the downward approach is adopted. Filling mining method mining. The basic parameters of mining, selection and smelting of mines are shown in Table 1.
2.2 The impact of different nickel prices on various indicators
According to the price of electrolytic copper in the market in recent years, according to the calculation of 50,000 yuan/t, considering the impact of different nickel prices, when the price of nickel is fluctuated from 60,000 yuan/t to 150,000 yuan/t, the average grade of mining is also allowed. From 0.3% to 1% fluctuation, according to formula (5), the cost and profit can be calculated separately, thereby obtaining the influence of different electric nickel prices and different mining grades on profits (see Figure 1).

The profit shown in Figure 1 includes the sales income of electric copper, which can get the following rules: 1 When the market price of electric nickel is constant, the average grade of ore can be increased within a certain range, which can increase profits; The intersection of the coordinates and the curves indicates the profit and loss balance of the electric nickel price represented by the curve. It can be seen that the price of electric nickel per ton rises from 60,000 yuan to 130,000 yuan, and the breakeven grade is derived from the grade. 0.95% was reduced to 0.39%.
From the cost point of view, the total cost is evenly distributed to the cost per ton of raw ore. According to formula (3), the relationship between the average nickel ore grade and the cost per ton of raw ore and the cost per ton of nickel is shown in Figure 2.

As can be seen from Figure 2, as the average ore grade increases, the cost of nickel produced per unit of ore continues to increase, while the cost per unit of nickel, that is, the price of nickel at breakeven, continues to decrease.
3 conclusions
The change of mineral product price affects every link in the production and operation activities of mining enterprises. Based on the break-even analysis method, the paper comprehensively considers the whole process of mining, mineral processing and smelting process, and derives the relationship model of grade, price and profit, and combines Jinchuan. Nickel ore, a brief description of the application of the model in mining enterprises. The results show:
(1) When the price of mineral products rises, the grade of the mine at the time of break-even is reduced, and the profitability of the company is continuously enhanced. The mining enterprises can continuously adjust the grade indicators and dynamically guide the mining activities.
(2) When the price of mineral products fluctuates little, the different ore grades have a greater impact on the cost. With the increase of the grade of ore, the cost per ton of ore metal smelting is increasing, and the corresponding unit smelting metal The cost is constantly decreasing.
Using this model, it is possible to visually reflect the impact and trend of mineral product prices and grade indicators on business indicators such as costs and profits to guide decision-making.
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