Optimization technology for group hole drainage of coal mining above deep high pressure and low permeability limestone aquifer

: Drainage for decreasing water pressure is one of the effective measures to prevent and control water disaster caused of coal mining above high pressure limestone aquifer. The deep limestone aquifer in Huaibei mining area generally has the characteristics of high water pressure, low permeability and uneven water abundance so it is generally difficult to meet the requirements for single-hole drainage. In order to achieve the best drainage effect and consider the requirements of engineering quantity and environmental protection, a multi-objective group hole drainage optimization model was established, which takes the minimum of single-hole flow rate and hole number as the objective function and the requirements of drainage borehole and water level control point drawdown as the constraint conditions. And the particle swarm optimization algorithm was used to solve the model. On this basis, the influence of permeability coefficient and water storage coefficient on the calculation results was discussed. The results show that the permeability coefficient and water storage coefficient have great influence on the optimization of single-hole flow rate and the number of holes. For the low permeability aquifer, measures such as using partially penetrated well, appropriately increasing the number of drainage boreholes and reducing the single-hole flow rate have good drainage effect. And the drilling work amount and total drainage amount are relatively small. These are all good layout schemes for drainage. According to the results of optimization, the drainage of a coal face in Huaibei was guided and achieved good results.

mining of lower coal group in Huaibei mining area and achieved good results.
The existing data show that the deep Taiyuan aquifer in Huaibei mining area has the characteristics of "high pressure and low permeability" (Chen et al.,2012;Zheng,2018). Due to the poor permeability of the aquifer, the water pressure decreases rapidly, with a large drop depth. The shape of the drain funnel is V-shaped, with a small impact radius. In order to improve the drainage effect, measures such as infill drainage borehole are generally taken. However, the increase of drainage borehole has increased the production cost of coal mines, and at the same time, drainage has also brought certain damage to groundwater resources. This has a serious impact on the sustainable development of the mining area. Therefore, under the condition of satisfying safe production, the total amount of water drainage and the amount of drilling work should be reduced to the greatest extent, thus achieving the best balance among safety, economy and environmental benefits. This is the fundamental starting point for the optimization of the drainage project.
As far as the author knows, there are many research results on optimal design in water resources management and other aspects at present (Song et al.,2016;Zhao and He,2015;Ali and Kavehkhalili,2015;Andrea et al.,2011). However, there are few research results on optimal design of drainage for decreasing water pressure of limestone in coal mine floor. However, there are few research results on the optimal design of drainage for decreasing water pressure of limestone in coal mine floor . Meng Lei (2015) established the optimal design model of single-hole drainage and gave the optimal layout of drainage borehole (Meng et al.,2015). As mentioned above, the limestone aquifer in deep mining generally has the characteristics of high water pressure, low permeability and uneven water abundance, and it is generally difficult to meet the requirements for single-hole drainage. However, no literature has reported on the optimization of group hole drainage in such aquifers. Therefore, the purpose of this study is to fill up this knowledge gap by optimizing the number of boreholes and the flow rate of boreholes in the group hole drainage , so as to ensure that the goal of drainage is achieved while effectively reducing the cost of coal mining and the degree of damage to the ecological environment. The optimization model proposed in this paper can be used to study the design and calculation of group hole drainage considering the hydrogeological characteristics of aquifer.
If the confined aquifer is in accordance with Theis assumption, when it is partially penetrated well and the straight-line distance r between the observation point and the drainage borehole is ≤ 1.5M, the drawdown equation is as follows: (1) Among them: . !
(4) Where, Q is the water discharge of the borehole, r is the straight-line distance between the calculation point and the drainage borehole, S is the water level drawdown; K is the permeability coefficient of aquifer; M is the thickness of the whole aquifer; u* is the elastic release coefficient; ( ) is the fully penetrating well function of Taisi; is the independent variable of well function; ζ is the additional resistance coefficient of non integrity; d is the distance from the aquifer roof to the top of the drainage borehole filter; l is the distance from the aquifer roof to the bottom of the drainage borehole filter; z is the distance between the aquifer roof and the bottom of the water level observation hole, i.e. the opening position; t is the drainage time.
It can be seen from formula (1) that the drawdown of partially penetrated well consists of two parts. The former represents the corresponding fully penetrating well drawdown, while the latter represents the additional drawdown caused by streamline bending near the pumping well due to the incompleteness of the pumping well. When the drainage borehole completely penetrates the entire aquifer thickness, the borehole is the fully penetrating well. Or when the straight-line distance r between the observation point and the center of the drainage borehole is > 1.5M, the additional resistance coefficient can be ignored and simplified as the corresponding fully penetrating well formula, and the drawdown equation is transformed into:

= 4 [ ( )]
(5) When the group holes drain water, the water quantity is Q1, Q2, ... Qn respectively. The head drawdown at any point can be calculated according to the seepage superposition principle, that is, it is equal to the sum of the head drawdown of each single drainage borehole, as shown in the following formula.

Optimization problem 2.2.1 Water level control point and its safe water level
In order to achieve the goal of safe mining, the aquifer is drained at a certain flow rate and lowered below the " secure hydraulic head". The secure hydraulic head value is the key index of drainage mining. The secure hydraulic head refers to the water head pressure that the coal seam floor aquifuge can bear. The smaller the secure hydraulic head value is, the larger the head to be reduced is. If the secure hydraulic head value is greater than the actual hydraulic head value, the mining under pressure can be carried out directly without discharging water. In actual project, the method of water bursting coefficient is generally used to determine the secure hydraulic head of working face, as shown in formula (7). p=TsM (7) Where, M is the thickness of the aquifuge, and the unit m, Ts is the critical water inrush coefficient. According to the "detailed rules for the prevention and control of water in coal mines", Ts is taken as 0.06mpa/m in the section with structural damage and 0.1mpa/m in the complete section.
In the actual drainage project, the boundary of the covering working face is taken as the drainage boundary, and the end point of the working face is selected as the water level control point within the drainage boundary to calculate the safe water level. First, determine the elevation Hd of coal seam water-resisting floor (the elevation of the aquifer roof) at each water level control point and initial water level elevation H0. Then the safe water pressure is converted into a safe water level by using the formula Hs=p×100+Hd. Finally, using the formula Ss= H0-Hs, the safe water level drawdown at each water level control point is obtained.

Optimization model
(1) Objective function In view of the high pressure and low permeability limestone aquifer, according to the previous description, the single-hole flow rate and the number of drainage boreholes are taken as the objective functions in the optimization model. That is, under the condition of water level drawdown and other constraints, the minimum single-hole flow rate and the number of drainage boreholes are reached, thus protecting groundwater resources to the maximum extent. The objective function can be expressed as follows: The drainage roadway is generalized as a line segment, and its dip angle is θ. When the coordinates of points a and b at both ends of the drainage roadway are (xp1，yp1) and (xp2，yp2), the roadway linear equation y=ax+b can be obtained. Where a is the slope of the straight line, b is the intercept of the straight line, and [xp1,xp2] is the abscissa range of the straight line segment. The total length of roadway is recorded as L.
There are n drainage boreholes arranged in the drainage roadway, which are F1,F2..Fi..Fn. They are arranged according to equal spacing, and the spacing between adjacent boreholes is D. The coordinates of any drainage borehole are (xci,yci). There are m water level control points in the working face, which are C1, C2…Cj, Cm, coordinate of any control point is (xj,yj). The distance from any drainage borehole to any water level control point is recorded as rij. It is assumed that the discharge capacity of each drainage borehole is equal, all of which are Q. The drainage borehole and water level control points are shown in Fig. 2. Then the minimum optimization models of Q and n are min (Q) and min(n).

Fig. 2 Layout diagram of arrangement of drainage borehole
On the premise of safe mining, the single-hole flow rate and the number of boreholes are minimized. Then the best position of the drainage borehole in the roadway will directly affect the realization of the optimization goal.
(2) Constraints condition : 1) Constraint condition of hole number As shown in Fig. 2, the lower left corner of the roadway is set as the layout position of the first drainage borehole (x1,y1). In addition, the drainage borehole shall not exceed the scope of drainage roadway. According to the coordinates of the roadway end points and the roadway straight line equation, the constraint conditions for the number n of drainage borehole in this group hole can be written as follows: 2) Constraint conditions of flow When the water level of the drainage borehole drops to the aquifer roof (Smax), the drainage flow of the borehole is recorded as Qmax. The flow rate is the maximum value constraint condition of single-hole flow rate in optimization, that is, the upper limit value of flow rate. If the radius of the drainage borehole is rw, considering the mutual interference between the drainage holes, the flow constraints are as follows: • When the drainage borehole is a full penetrating well or a partially penetrated well but the distance D between boreholes is not less than D≥1.5M, the i-th drainage borehole is: (10) • The drainage borehole is a partially penetrated well. If the distance D between boreholes is less than 1.5M ,when the mutual interference of the non-integrity additional resistance coefficient ζ is not considered, the i-th drainage borehole is: Drainage roadway ≤ 4 ( ( −1) ) + ⋯ + ( ) + ( ) + ( ) + ⋯ + ( ( − ) ) + ( , , , ) (11) 3) Constraint conditions of water level drawdown at control points The drawdown of water level at all control points shall reach the purpose of safe mining. For any j-th water level control point, the safe water level drawdown is , and its constraint conditions are as follows: • When the drainage borehole is a full penetrating well or a partially penetrated well but ≥ 1.5M, there are: (12) • When the drainage borehole is a partially penetrated well and the straight-line distance r between the water level control point and the drainage borehole is ≤ 1.5M, there are: In view of the problem of drainage of limestone aquifer with high pressure and low permeability, due to the strong heterogeneity of aquifer water abundance, the form of infilling drainage borehole is generally adopted to realize the safe mining in the whole working face. However, if too many boreholes are constructed, the mining cost will be increased. If the boreholes are reduced, the water discharge of single hole will be increased. However, due to the characteristics of low permeability, single hole drainage should not be too large, otherwise the effect of drainage is poor. Therefore, the objective of this optimization is to construct the least drainage borehole and minimize the single-hole flow under the constraint conditions, which is a multi-objective optimization problem. In this paper, multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the problem. This algorithm was proposed by Coello et al in 2002 (Coello andLechuga,2002), which extends particle swarm optimization to multi-objective optimization design. This algorithm has been recognized as a classical multi-objective particle swarm optimization algorithm. The core of this algorithm is how to choose the best pbest in history. For multi-targets, the comparison of two particles can't compare which one is better. A particle is better if each of its targets is better. If some are better and some are worse, it is impossible to say which is better or which is worse strictly. For multiple objectives, there are many optimal individuals. Each particle can only choose one as the best individual in the algorithm. The flow chart of MOPSO algorithm is shown in Fig. 3 (a), and the establishment and calculation flow of this optimization model is shown in Fig. 3 (Fig. 4). There are 12 layers limestone (L1-L12) in the Taiyuan formation of mine field ,The total thickness of Taiyuan formation is 85-130m. And the accumulated thickness of limestone is 45-70m, accounting for 60% of the total thickness of Taiyuan formation. The aquifer of upper 1-4 layers limestone (L1-L4) is the main factor affecting the safe mining of the No. 10 coal seam. The aquifer below the 5 layer limestone is far away from the No. 10 coal seam. Therefore, the impact on mining is small.
The mine stratum trend is nearly north-south, inclines to east, with an inclination of about 10°, and presents monoclinal structure. Faults are developed in the mine field, most of which are tensional and torsional faults. No large amount of leakage of flushing fluid was found in fault fracture zones of different horizons during drilling. The pumping test data of fault zone show that the unit water inflow q=0.016-0.00048L/(s.m), the permeability coefficient K=0.023-0.0017m/d, the water inflow is small, and the aquifuge meets the standard. Due to the water blocking effect of faults, the water-bearing rock group in the upper member of Taiyuan formation in the mine field is a closed and weak aquifer, which provides feasibility for drainage for decreasing water pressure mining. As can be seen from Table 1, q=0.0052-0.773 L/(s.m), K=0.026-3.93m/d , with strong water abundance and connectivity at the shallow concealed outcrop, gradually weakening to a weak permeable layer towards the deep. In addition, the q and K values of different boreholes are quite different, which further illustrates the heterogeneity of water abundance and permeability of the upper limestone aquifer of Taiyuan formation. The karst fissure aquifer in deep mine has the characteristics of high pressure and low permeability.
1013 and 1011 working faces are located in 101 mining area, which is divided into several blocks by several large faults F9, F10 and F11. The two working faces are located in the middle of F9 and F10 faults (Fig.  4), and the hydrogeology conditions are relatively independent. Under the working face lies the high pressure limestone aquifer of Taiyuan formation, in which the thickness of L1-L4 aquifer is 50m. Among 126 water exploration boreholes in the upper part of the Taiyuan formation limestone (L1-L4) aquifer in the mining area, there were only 4 boreholes with water output of more than 5m 3 /h, most of them were dry holes, and the water output rate was less than 2%. It was further confirmed that the limestone aquifer on the bottom plate is insufficient in supply and has good drainage. Since the mine was put into operation in 2007, the limestone aquifer of Taiyuan formation has been drained. Before the mining of the two working faces, the water level elevation of Taiyuan limestone water level observation hole 14-observation 1 hole in the mining area is -50m, and the minimum aquifuge thickness of coal seam and aquifer is 45m. According to the calculation of the lowest elevation of the working face -515m, the maximum water pressure on the bottom of the aquifuge is 4.65 MPa, and the water bursting coefficient is about 0.103, which is greater than the critical value in the "detailed rules for the prevention and control of water in coal mines", so it is dangerous for water inrush. It is planned to use 1 year for drainage for decreasing water pressure, and the goal is to reduce the water pressure to the critical water bursting coefficient value, so as to ensure safe mining.
According to the drainage characteristics of limestone aquifer in Taiyuan formation with high pressure and low permeability, in order to ensure the smooth mining of the two working faces, a special drainage roadway was constructed in the mine (Fig. 5). Through the construction of drainage borehole, the purpose of drainage mining was achieved. The floor elevation of the drainage roadway is -541.9--540.7m, with a total length of 390m. The following will carry out the optimization calculation of the drainage borehole in the drainage roadway. According to the hydrological exploration report, the aquifer thickness of L1-L4 in the mining area is 50m, the permeability coefficient K is 0.03 m/d, and the water storage coefficient is 1×10 -6 . The radius of drainage borehole rw is 0.05m, and the maximum drawdown of single hole Smax is 490m.

Establishment and solution of optimization model
According to the selection principle of water level control points, the end of the upper and lower roadway far away from the drainage borehole and the working face with large buried depth is the control point, as shown in Fig. 1. Each control point is the observation point of water level, which is the water pressure at the bottom of the aquifuge of the coal seam floor, i.e. z=0, and d=0 of the drainage borehole. To facilitate calculation, take the lower left corner of Fig. 5 as the coordinate origin, and get the relative coordinates of each control point as shown in the table below. According to the detailed rules for the prevention and control of water in coal mines and the mining practice in Huaibei, the critical water bursting coefficient of the working face is 0.06MPa/m, and the safe water pressure at the control point is 2.7 MPa. According to the water head formula, the safe water level at the control points and the safe water level drawdown at each control point are shown in Table 2. The drainage borehole is planned to be arranged in section AB of the roadway. According to the coordinates of A(2008.42，582.83) and B(2146.8，408.48), it can be concluded that the roadway can be generalized into a linear equation as y=-1. 23x+3057.4(2008.42≤x≤2146.8). According to the formula (1) and (2) of the optimization model, the model is solved by using the multi-objective particle swarm optimization algorithm based on Matlab software, and the calculation results are shown in Table 3. Fig. 6 is the solution of all the constraints given by the example of a fully penetrating well. The program gives the final result according to the optimization objective of small number of holes and small flow of single hole, combined with the principle of minimum total flow.  Fig. 6 Solutions for all constraints of a fully penetrating well It can be seen from Table 3 that when the drainage borehole is a fully penetrating well, the optimal number n n*Q (m of drain holes is calculated as n=4, the spacing between holes is 62.17m, the discharge of single hole is 131.05m 3 /d, and the total discharge is 524.2m 3 /d. When it is a partially penetrated well, with the decrease of l/M, that is to say, the smaller the degree of drilling through the aquifer, the more n, the larger the increase, the smaller the single hole flow and the little difference in the total flow. However, the total amount of drilling work shows the trend of decreasing step by step. For the low permeability heterogeneous aquifer, from the above, through the infilling drilling, single hole small flow can achieve better drainage effect. However, when the flow rate of single hole is small, there are many holes and high construction cost. At the same time, the aquifer is a composite aquifer composed of L1-L4. Generally, the water abundance of L3-L4 is better. If the l/M is smaller, there is a problem that it is difficult to enter L3-L4 by drainage borehole. According to the results of this optimization calculation, when l/M=0.6, the number of holes, the amount of drilling work is moderate, and the total water discharge is also the smallest, which is an ideal water discharge design scheme.

Parameter discussion
(1) Aquifer permeability In order to study the influence of aquifer permeability on drainage, when the fixed water storage coefficient u* is 1×10 -6 and the permeability coefficient K value is between 0.008m/d-0.1 m/d, the optimal n and Q are obtained respectively, as shown in Fig. 7. It can be seen from Fig. 7 that with the gradual increase of K, the low permeability of the aquifer changes from low to high, and n shows the phenomenon of first decreasing and then rising, and n is the smallest when K=0.03m/d. This shows that the effect of drainage in low permeability aquifer is better when the measures such as infilling drainage hole and reducing single hole flow are taken. In addition, with the increase of K value, the flow rate Q of single hole increases generally, but when K value reaches a certain high value, with the increase of n, the growth of Q appears gentle. (2) Water storage coefficient of aquifer In order to explore the influence of water storage coefficient on the optimization results, when the fixed permeability coefficient K=0.03m/d and the water storage coefficient u* value is between 0.1×10 -6 -15×10 -6 , the optimal n and Q are obtained respectively, as shown in Fig.6. It can be seen from Fig. 6 that the water storage coefficient reflects the water rich degree of the aquifer. Therefore, with the increase of the water storage coefficient, the number of the optimal drainage holes under the constraint conditions is also increasing step by step, while the single hole flow rate is decreasing step by step, and the total flow rate is increasing step by step.

Drainage effect
In the actual drainage engineering design of the mine, the optimization results are used for reference, the partially penetrated well scheme is adopted, the single hole flow is reduced, the drainage borehole is properly densified and other measures are taken to deal with the drainage problem of the heterogeneous and low permeable limestone aquifer. In the two drilling fields of the drainage roadway, 6 cross limestone layer drainage boreholes are arranged (Fig. 8). Except that the final hole of F1-2 is in the limestone of the third Taiyuan formation, the other five drainage boreholes are all in the limestone of the fourth Taiyuan formation. The single hole discharge is concentrated between 52m 3 /d and 100 m 3 /d. In addition, in order to achieve better drainage effect, four nearly horizontal drainage boreholes were constructed along 170 °,196 °,206 ° and 222 ° azimuth in No. 3 drilling field of drainage lane. The drainage boreholes are basically parallel to the limestone trend of the fourth Taiyuan formation, with an average length of 140m. water level change of 14 observation 1 hole As of December 31, 2015, the total discharge of limestone in Taiyuan formation of mining area 101 is 50m 3 /h, with a total discharge of about 490000 m 3 . The water level of 14 observation 1 (outside the outcrop of the mining area) in the limestone observation hole of Taiyuan formation on the ground decreased from -50m to -170m, with a cumulative decrease of 120m, as shown in Fig. 8 (b). The maximum daily decline is 2.4m. The water pressure of the underground pressure tap in the working face is 0.2MPa (corresponding to the water level of -320m, and the elevation of the lowest point of the working face mining section is -401.1m, and the maximum water bursting coefficient of the working face is 0.026 MPa/m, basically reaching the goal of drainage mining.
It is worth noting that the optimization model of multi hole drainage in this paper is based on the unsteady flow theory of vertical well. For the inclined shaft in the actual project, the conversion method is often used to calculate the drawdown, which has calculation errors. At the same time, the model in this paper is not suitable for the calculation of drawdown of horizontal drainage borehole. At the same time, the model in this paper is not suitable for the calculation of the drawdown of horizontal drainage hole along the limestone layer. However, the optimization model in this paper still has certain guiding significance for the determination of single-hole flow rate, the degree of drainage borehole penetrating the aquifer and the number of holes when it is applied to the drainage of low permeability aquifer.

Conclusion
In the deep mining, limestone aquifer is characterized by high water pressure, low permeability and uneven water abundance, so it is difficult to meet the requirements of single hole drainage. Based on the characteristics of low permeability of aquifer and the requirements of economy and environmental protection, this paper establishes a multi-objective multi hole drainage optimization model, which takes the single-hole flow rate and the minimum number of holes as the objective function, and takes the requirements of drainage boreholes and the drawdown of water level control points as the constraints. and is applied to a coal mining face in Huaibei. The main conclusions are as follows: (1) When the degree of drainage borehole penetrating the aquifer (l/M) is smaller, the number of optimized water drainage holes n increases gradually, and the increasing range increases gradually. The single-hole flow rate gradually decreases, but the total flow rate has little difference. At the same time, the total amount of drilling work shows the trend of decreasing step by step. In view of the low permeability heterogeneous aquifer, it is a better drainage design scheme to use the partially penetrated well, increase the number of drainage boreholes, reduce the single-hole flow rate and other measures appropriately, with better drainage effect, and relatively small drilling quantities and total drainage.
(2) The hydrogeological parameters have great influence on the optimization results. With the increase of the permeability coefficient K of the aquifer, the number of the optimal drainage boreholes decreases first and then increases, while the single-hole flow rate Q increases monotonously, but the increase tends to decrease. With the increase of water storage coefficient, the number of optimal drainage boreholes increases step by step, and the single-hole flow rate decreases step by step.
(3) According to the characteristics that the upper aquifer of Taiyuan formation is a compound aquifer composed of L1-L4 and the lower L3-L4 has good water-abundance, it is suggested that the incomplete well should penetrate through the third layer of limestone in the actual drainage project. In addition, for the mine with limestone drainage roadway, the drainage borehole along the limestone layer can be constructed in the roadway. Better drainage effect can be achieved by combining with conventional through layer drainage hole