Water Resources Utilization and Protection in the Coal Mining Area of Northern China

This study investigates multiple types of water resources in the western mining area in China, their supply-demand balance by using the same dimension gray recurrence dynamic model GM (1, 1), and water content coefficients of mines to ease water supply-demand contradiction. A multi-objective programming model is proposed for optimal water resources allocation management. Optimal technical schemes for water resources allocation among different users are obtained. The optimization model improves upon the previous studies by using water demand and water supply forecast. Coordinated development for mining safety, mine water utilization, and remediation and control of water environment is achieved.

fairness, priority, efficiency and comprehensive benefits. Also, it is useful for enhancing the economic and social benefit and ecological environment protection 44,45 . For examples, Wu (1995) derived a comprehensive theory of mine water utilization, named "balance of drainage and water-supply for environmental protection", which was successfully applied in Jiaozuo coal mine in China 46 . Management of mine water resources in the mine areas currently mainly focuses on multi-objective decision-making, while direct forecast of water demand and mine water drainage (which was routinely used many years ago) are insufficient for multi-objective optimal management of water resources in coal mines 47,48 . This study uses the Dongsheng coal mining area as an example to derive the multi-objective model for water resources optimal management in coal mines in northern China. The Dongsheng mining area, located near the contiguous zone in the north of Shaanxi Loess Plateau and southeast of Maowusu desert, is one of the world-class coal production bases in China. Continuous increasing of development scale of coal resources in this area has caused the changes of aquifer structure and conditions of groundwater recharge, flow and discharge, which in turn results in significantly declined water levels, dry aquifers, reduced or even disappeared flow of some springs 49 . These are due to decreased precipitation and increased mine drainage and water consumption of agriculture and industry every year. All of them lead to the contradiction among the water demand increase of the coal industry and other energy and chemical industries, the shortage of regional water resources, and protection of eco-environment in the mining areas 50 . Therefore, the study on water resources protection and optimal management is of vital importance for the sustainable use of water resources and balance environmental protection and industrial development in these regions.
In this study, a multi-objective optimization management model is developed to obtain optimal solutions for water resources utilization constrained by quantities of surface water, groundwater, and mine water in Dongsheng mining area. It is of great significance for rational development, comprehensive utilization and scientific management of water resources in the study area. The results are helpful for providing references for water resources protection and management in coal mine areas in the arid or semi-arid zones.

Material and Methods
Study area. The study region, Dongsheng mining area, has an area of over 500 square kilometers ( Fig. 1), where three kinds of water resources are available, including surface water, groundwater, and mine water. Surface water includes the Wulanmulun river, lakes, reservoirs, ponds, and some other surface water bodies. Mine water includes mine water drainage from mines Daliuta, Huojitu, Shangwan, Bulainta, Halagou, Shigetai, and Wulanmulun.
Multi-objective optimization model. The multi-objective optimization model aims to systematically consider water sources allocation, including water quantity, water quality, and the characteristics of main water users, to achieve the highest water supply guarantee rate and the lowest cost of water supply. The decision variables are the supplied water amounts from various water sources to different water users in different sub-regions.
The study area is divided into eight sub-regions, including Daliuta, Bulianta, Shangwan, supply system of coal liquefaction, Halagou, Wulanmulun, Shigetai, and Huojitu. The water users include production, living, industry, and virescence. The water sources include tap water, industrial reuse water, and virescence recycled water. The number of decision variables in the study area is 96 (8 × 4 × 3). The multi-objective optimization model of water resources in the mining area has two objective functions.
Objective 1: to meet the maximum water-supply needs of each sub-region.
Objective 2: to minimize the total water supply cost in the study area. where f 1 (x) is water supply amount in the study area; f 2 (x)is the total water supply cost in the study area; x ijk is the amounts of water supply from water source i to user j in sub-region k; α j is the cost coefficient of unit water supply from water source j; i is index for the number of water source types (i = 1, 2, 3); j is index for the number of water user types (j = 1, 2, 3, 4); and k is index for the number of the sub-region (k = 1, 2, …, 8). Constraint conditions are the law, rules, and regulations the model relies on when seeking the solution, only under the definite constraint conditions, the calculation results are effective. The present model has 5 constraints: (a) constraints of water demand The largest supply of water should not be greater than 120% of water demand on the basis of meeting the needs of each user, in order to save water and reduce water supply costs. Water demand constraints include water demand constraints of production, living, industry, and virescence as follows: Scientific RepoRts | where Q k−1 is water demand for production; Q k−2 is water demand for living; Q k−4 is water demand of virescence. (b) constraints of water supply capacity of each sub-region  where Q T-W is water supply capacity of the tap water; Q I-W is water supply capacity of each mine's own independent water resource; Q R-W is total water supply capacity of industrial reused water; Q V-W is total water supply capacity of virescence recycled water. (c) constraints of water quality Contaminants need to meet emission standards and cannot exceed the total emissions.
where C kj r is the concentration of pollutant r from user j in sub-region k; C r 0 is the standard concentration of pollutant r for pollutant discharge; W 0 is total permitted pollution discharge capacity. (d) non-negative constraints of decision variables The decision variables involved in the optimation calculation, i.e., the water supply to different users in different subareas should be bigger or equal to zero. (e) zero constraints of decision variables Following the standard of modeling and the principle of water supply by quality, formula (12) expresses that the reused water for afforestation is not used in production, livelihood, and industry, its corresponding variable is zero and not involved in the optimization calculation formula (13) expresses that the industrial reused water is not used in livelihood, its corresponding variable is zero and not involved in the optimization calculation.
According to the objective of the current project, this paper has chosen the tool fgoalattain in Matlab to solve the multi-objective problem. fgoalattain solves the multiobjective goal attainment problem, which is one formulation for minimizing a multiobjective optimization problem 51 : where x, weight, goal, b, beq, lb, and ub are vectors, A and Aeq are matrices, and c(x), ceq(x), and F(x) are functions that return vectors. F(x), c(x), and ceq(x) can be nonlinear functions. The formulations for multiobjective optimization have been fully discussed in the Standard Algorithms chapter for showing how to use Matlab optimization toolbox [51][52][53][54] .

Results
Mine Water Discharge at National Level. According to the data of National Bureau of Statistics in China, during the 10 th to 12 th "Five-Year National Plan" periods (from 2005 to 2020), national wastewater discharge amounts have grown linearly by 10 billion m 3 per five-year. However, the growth of coal mine wastewater discharge amount has declined gradually, compared with the previous five-year plan (from 2001 to 2004). And the growth rate of coal mine wastewater discharge from the10 th to 12 th "Five-Year" has decreased by 169.2%, 32%, and 17.3%, respectively. At the same periods, the rate of national coal mine water utilization has increased by 35.2%, 59.2%, and 75.5%, respectively.
Water Resources Situation in the Study Region. There are rich coal resources but scarce water resources in northern China. With rapid social and economic development, regional conflicts between supply and demand of water resources have become increasingly prominent. The utilization of the available mine water includes simply mine water treatment and reuse for coal mining, which is far from the concept of coordinated development and optimal decision on environmental protection and utilization of mine water resources.
According to a field investigation conducted in October and December 2006 55 , the amount of surface water resources is about 1.197 × 10 8 m 3 , including about 1.17 × 10 8 m 3 of mean annual runoff of the Wulanmulun River. There are 47 surface water bodies including lakes, reservoirs, and ponds (Table 1), with a total water surface area of 5.91 × 10 5 m 2 and a total surface water volume of 2.70 × 10 6 m 3 , in which the Wulanmulun lake is the largest one with a water surface area of 4.0 × 10 5 m 2 and a volume of 2.2 × 10 6 m 3 .
The main recharges of groundwater in the study region are rainfall infiltration and lateral runoff, and the main discharges are spring discharge, coal mine water drainage and base outflow to the Wulanmulun river. The balance equation in the study area during the balance duration (one year) is: where Δε is the change amount of groundwater reserve; Q rf is the recharge amount from rainfall infiltration; Q lr is the amount of underground lateral runoff; Q spr is the amount of spring discharge; Q wi is the amount of coal mine water drainage; and Q bf is the amount of base outflow to the Wulanmulun river. For the study of regional water balance, generally it is necessary to select a complete hydrological year as the balance period, and median water year is the best for the hydrological year 56 . Thus, 2004 (from 1975 to 2018) was selected to conduct the study of water balance with precipitation guarantee rate of 50%. It can be calculated from the above formulas that the total amounts of recharge, discharge, and the change in water storage volume are 80.8, 82.29, and minus 1.49 million m 3 in this study area during the balance period, respectively ( Table 2). The recharge amounts from the rainfall infiltration and the lateral runoff are 75.98 and 4.82 million m 3 , respectively. The spring drainage, the mine water drainage, and the base outflow to the Wulanmulun river are 33.27, 12.43, and 36.59 million m 3 , respectively (Table 2). Groundwater budget is negative balance in the first year of the balance period, with a reduced amount of groundwater storage of about 1.49 million m 3 .
The mine water drainage of these seven coal mines is 1470.50 m 3 /h and the total annual amount is 12.43 million m 3 (Table 3), which are increasing year by year. In addition, the total surface water area in these seven mines is 130.63 million m 2 and the total volume is 39.31 million m 3 . Therefore, the mine water resources have great potential to be exploited and utilized as an alternative water source.
According to the analysis above, the total volume of water resources of surface water and groundwater in the study region is 130.64 million m 3 , which was calculated by the sum of the amount of surface water resources  Table 4 shows that the probability of small error, P is bigger than 0.95, the variance ratio, C is smaller than 0.35, indicating that the fitting accuracy meets the standard of class one 57 .
As shown in Table 5, both C (<0.35) and P (>0.95) of each year of the prediction meet the standard of class one. According to the principle of posterior error test, when the development grey number, a, of GM (1, 1) is smaller than 0.3, the model can be used in medium and long term prediction. Parameter a listed in Table 5 is all smaller than 0.1, which means that GM (1, 1) model has some practical value, and can be used in long-term prediction.
Demands of all kinds of water resources will increase from 4.86 × 10 4 m 3 /d in the first year (2005) of the balance period to 11.68 × 10 4 m 3 /d in 2020, in which tap water demand increases by 4.24 × 10 4 m 3 /d, and industrial recycled water demand increases by 1.86 × 10 4 m 3 /d (Fig. 2).

Name Daliuta Huojitu Shangwan Bulianta Halagou Shigetai Wulanmulun Sum
Water surface area (m 2 ) 6820.  The water supply amount is predicted during the balance period, which increases from 8.33 × 10 4 m 3 /d in 2005 to 1.03 × 10 5 m 3 /d in 2010, then remains roughly constant at 1.03 × 10 5 m 3 /d from 2010 to 2015, and finally decreases to 9.93 × 10 4 m 3 /d in 2020 (Fig. 3). The predicted water supply yield rooted mainly in the "Eleventh Five Years Plan" and the Prospect Objective to 2020 of Coal Industry of Shendong Branch of China Shenhua Coal Group Corporation". In terms of the proportion of water supply, the proportion of tap water supply will decrease from 71% in the first year to 56.8% in the fifteenth year, while the proportion of industrial recycled water supply will increase from 29.1% in the first year to 43.2% in the fifteenth year. Therefore, the results indicate that the utilization rate of mine water resource will increase in the future, which can not only alleviate the contradiction between supply and demand of water resources, but also save money and improve the enterprises' economic and social benefit.
Water Yield of Mine Prediction. The mine water was predicted by using the water content coefficient of mine, one of the hydrogeological analogy methods 58 : p where K p is the water content coefficient of mine; Q(t) is the mine water drainage quantity, and P(t) is the coal yield in the same period (usually a year). The prediction results of mine water are shown in Fig. 4, which indicates that mine water drainage will increase yearly in each mine of the Shendong mining area. The total drainage amount will increase from 4.39 × 10 4 m 3 /d in 2005 to 6.92 × 10 4 m 3 /d in 2020.    Optimal Allocation of Water Resources. In view of the water supply and demand conditions in Shendong mining area, a multi-objective decision analysis was conducted to deal with the contradiction of water use in each mine, and determine the optimal allocation of water resources. The water supply in the study area is mainly composed of groundwater provided by the water source of each spring area, surface water; mine water and reuse water are provided by domestic sewage treatment plants.
According to the current water use mode of the mining area and water quality, water resources are divided into tap water supply, industrial reuse water, and virescence recycled water. Among them, industrial reuse water is composed of mine water reuse water, mainly for industrial, production and other water sectors in the study area; virescence recycled water is composed of the treated domestic sewage from Daliuta and Heitagou domestic sewage treatment plants, Liuta and Huojitu underground water treatment plants for watering lawns and trees. The water quality was used to classify the water resources in this work.
In order to realize the full utilization of water resources and to achieve cost minimization on the basic of the water supply to meet the demand in the mining area, the priority sequence was carried out according to the users. In other words, the demand for production was given priority, followed by the demand for life, industry, and irrigation.
The water demand data of each user in the sub-district in 2008, 2010, 2015, 2020 and the water supply capacity data of each water source were brought into constraints of the previous section, and a constraint matrix was formed. Then, the constraint matrix was substituted in the multi-objective programming function fgoalattain of Matlab as a parameter.   The solutions of multi-objective optimization model were obtained with acceptable tradeoff among the major variables. Due to the limitation of space, not all the results could be enumerated one by one. So, the result of Daliuta (k = 1) is listed in Table 6 as a representative. In general, the total water supply in 2008, 2010, 2015 and 2020 can meet the water demand of production, domestic, industry and virescence. In 2008, industrial reuse water can meet the requirements of production water demand in the case of non-use of tap water; all domestic water comes from tap water; if the mine does not use tap water, the remaining industrial reuse water can also fully meet the requirements of industrial water demand; all irrigation water comes from the use of the mine's own virescence recycled water. In 2010, industrial reuse water can meet the requirements of production water demand, in the case of a small amount use of tap water; all domestic water comes from tap water; even if all the remaining industrial reuse water is used for industry, 5375 m 3 /d tap water is still needed to meet the industrial water demand; all irrigation water comes from the use of the mine's own virescence recycled water. In 2015, industrial reuse water can meet the requirements of production water demand, in the case of a small amount use of tap water; all domestic water comes from tap water; even if all the remaining industrial reuse water is used for industry, 5348 m 3 /d tap water is still needed to meet the industrial water demand; all irrigation water comes from the use of the mine's own virescence recycled water. In 2020, industrial reuse water can fully meet the requirements of production water demand; all domestic water comes from tap water; even if all the remaining industrial reuse water is used for industry, 6413 m 3 /d tap water is still needed to meet the industrial water demand; all irrigation water comes from the use of the mine's own virescence recycled water.

Discussion and Conclusions
The work analyzed water resources situation in the study region, including the distribution of water resources, did regional groundwater balance calculation, used GM (1, 1) to predict water demands in the following 15 years, and build a multi-objective programming model for optimal water resources allocation management.
In general, national wastewater discharge amounts, coal mine discharge amount, production of coal, utilization amount of coal mine waste, and national rate of coal mine water utilization have linearly increased. The total volume of water resources is 130.64 million m 3 in the study area, with the amounts of surface water, groundwater, and mine water of 119.7, 80.8, 12.43 million m 3 , respectively. By analysis of groundwater budget, water storage volume decreased by 1.49 million m 3 in the balance zone during the balance period.
The tap water and industrial recycled water demands in the following 15 years are forecasted by a same dimension gray recurrence dynamic model GM (1, 1) (Fig. 2), where the supply amounts of tap water and industrial water are used as original data. Demands of all kinds of water resources will increase year by year, the total amount of water demand increases from 4.86 × 10 4 m 3 /d in the first year of balance duration (2005) to 11.68 × 10 4 m 3 /d in 2020, in which tap water demand increases by 4.24 × 10 4 m 3 /d, and industrial recycled water demand increases by 1.86 × 10 4 m 3 /d. All water demands including domestic, agriculture, industry and mine water consumption, are increasing year by year by a dynamic gray model GM (1, 1). The forecasted mine water drainage is increasing yearly on every mine in the Shendong area by using the hydrogeological analogy method, from 5.13 × 10 4 m 3 /d in the third year to 6.92 × 10 4 m 3 /d in the fifteenth year.
The optimal technical schemes among different users are acquired from all nine technical schemes through the application of a multi-objective programming model. The optimal technical schemes among different users are acquired from all nine technical schemes through the application of a multi-objective programming model. By analyzing the results of 2008, 2010, 2015, 2020 optimization calculations, it can be concluded that the total water supply can meet the total water demand in 2008, 2010 and 2015, and the total water supply can't meet the total water demand in 2020; a shortage of tap water could occur in 2015 and 2020, and the shortage of tap water is increasing year by year. In general, the total water supply in 2008, 2010, 2015 and 2020 can meet the water demand of production, domestic, industry, and virescence.