Simulation Method And Application Of Groundwater Flow Field Of Coal Mine Based On The Subdomain-Analytic Element Method

Coal resources occupies the largest proportion in China’s energy structure,and based on the characteristics of China’s energy resources and the security considerations of the national energy strategy,the dominant position of coal resources will not change in the short term.Coal mine water hazard is one of the main mine hazards that threaten coal mine safety production.At present,the simulation methods of coal mine groundwater flow field are mainly divided into two types:analytical method and numerical method.The analytical method has many restrictions on the shape of flow field,and the model is often difficult to reflect the actual hydrogeological conditions of coal mine.Numerical methods such as finite difference method and finite element method are not flexible enough for model adjustment and have high computational cost.In view of the many problems and deficiencies of the current coal mine groundwater flow field simulation methods,it is of great practical significance to explore a fast,efficient,accurate and reliable flow field simulation method that meets the actual needs of coal mine water hazard prevention and control.On this basis,the development of an open source simulation program based on this simulation method can modify or optimize the model governing equation and solution algorithm according to the actual needs of coal mine groundwater flow field simulation.In view of many problems of above-mentioned coal mine groundwater flow field simulation methods and in the implementation of model,this thesis explored the feasibility of applying the Subdomain-Analytic Element Method to coal mine groundwater flow field simulation through theoretical analysis and case studies,and developed an open source simulation program of coal mine groundwater flow field based on this simulation method.The Subdomain-Analytic Element Method is a new type of groundwater flow field simulation method developed on the basis of the Analytic Element Method.The basic principle of this simulation method is to superimpose solutions of partial differential equations for various hydraulic elements(such as flow field boundaries,pumping(injection)wells,transient flow,etc.)for the purpose of simulation of the flow field.The solution of the model is the superposition of analytical solutions,so the model accuracy is high.At the same time,the flow field model does not require meshing,so it can be modeled and adjusted quickly through parameter input.The Python language has the advantages of open source,free,easy-to-use,and strong scalability,as well as powerful third-party modules(such as NumPy,SciPy,Matplotlib,etc.)that can be used for scientific calculations and data mapping.Therefore,the Python language is particularly suitable for fast script writing and application program development.This thesis used Python language to develop an open source simulation program of coal mine groundwater flow field based on the Subdomain-Analytic Element Method.The main research contents and results of this thesis are as follows:(1)The Analytic Element Method is the theoretical basis of the Subdomain-Analytic Element Method.In view of the research needs of the Subdomain-Analytic Element Method,the core theories and methods of the Analytic Element Method were explained.On this basis,following the construction principle of line-sink complex potential function,the nonlinear density distribution high-order line-sink complex potential function was created whose density distribution expression is a high-order standard polynomial,and the spatial distribution law of complex potential,discharge potential,and stream function value of nonlinear density distribution high-order line-sink in the flow field where the line-sink is located was rigorously analyzed and demonstrated by mathematical methods.(2)The realization process of applying the Subdomain-Analytic Element Method to simulate the groundwater flow field was explained systematically,including division of subdomains,application of line-sinks to simulate inner and outer boundaries of flow field,simulation of transient flow using Multiquadric Radial Basis Function area-sinks,simulation accuracy control,etc.On this basis,combined with the research results of nonlinear density distribution high-order line-sink in Chapter 2,the general method of constructing a coal mine groundwater flow field model based on the Subdomain-Analytic Element Method was discussed in detail,including the simulation methods of various hydraulic elements in flow field(such as flow field’s inner boundaries,flow field’s outer boundaries,pumping(injection)wells,transient flow,etc.)and the generation process of flow field model’s system equation set.(3)The advantages of choosing Python language to develop open source simulation program of coal mine groundwater flow field based on the Subdomain-Analytic Element Method were elaborated in detail.How to use Class in Python to build the open source simulation program’s framework and the Python implementation method of the simulation of inner and outer boundaries of flow field and transient flow were discussed.Finally,the code showed how the program implemented various simulation functions of the flow field model.(4)The hydrogeological conditions and mine water filling conditions of the Danhou coal mine were studied,and the simulation range and boundaries conditions of the flow field model of the lower Ordovician limestone aquifer in the mine were determined.Applying the Subdomain-Analytic Element Method model’s construction method discussed above and combining the actual conditions of Danhou coal mine’s groundwater flow field,the Subdomain-Analytic Element Method flow field model of Ordovician limestone aquifer in Danhou coal mine was established.Several specific classes and methods of classes were added to the open source simulation program of the Subdomain-Analytic Element Method model developed above to meet the needs of limestone aquifer flow field simulation in Danhou coal mine.The identified and verified Ordovician limestone aquifer Subdomain-Analytic Element Method flow field model was used to predict the dewatering rate when mining No.5 coal seam of Danhou coal mine.Taking the water inrush coefficient 0.06MPa/m as the critical value,and under the condition that the total dewatering rate was 1300m~3/h(the dewatering rates of 22-24 and ck516 were 750m~3/h and 550m~3/h,respectively),the model operation results showed that the water level of Ordovician limestone aquifer in the mine was below the critical safe water level after 57 days.(5)In order to evaluate the simulation accuracy and computational efficiency of the Subdomain-Analytic Element Method model,the simulation results of the Subdomain-Analytic Element Method model,the MODFLOW model and the FEFLOW model were compared and analyzed from the calculation of water level of Theis well flow and the prediction of the dewatering rate of Ordovician limestone aquifer when mining No.5 coal seam of Danhou coal mine.The absolute deviations between the calculated water level of the Theis well flow and the exact solution of the Theis well flow of water level of the MODFLOW model,the FEFLOW model and the Subdomain-Analytic Element Method model are -0.15m～0.37m,-0.36m～0.13m,-0.09m～0.03m,respectively;and the proportions of the data whose absolute value of relative deviation that less than 0.05%are 38.85%,37.33%,and 100%,respectively.The water level of Ordovician limestone aquifer of the MODFLOW model,the FEFLOW model and the Subdomain-Analytic Element Method model in the mine dropped below the critical safe water level after 55 days,60 days,and 57 days,respectively.In the first 30 days of the drainage,the absolute deviation ranges of the water level of each water level control hole in the Subdomain-Analytic Element Method model from the MODFLOW model and the FEFLOW model at the same time are-15.75m～14.64m and-20.01m～29.42m,respectively;and the relative deviation ranges of that are-1.83%～1.78%and-2.33%～3.61%,respectively.Within 55 days to 60 days of the drainage,the absolute deviation ranges of the water level of each water level control hole in the Subdomain-Analytic Element Method model from the MODFLOW model and the FEFLOW model at the same time are -4.97m～4.39m and-5.46m～7.76m,respectively;and the relative deviation ranges of that are-0.62%～0.51%and-0.68%～0.98%,respectively.It can be seen that the water level of the Subdomain-Analytic Element Method model is generally lower than that of the MODFLOW model and higher than that of the FEFLOW model in the early stage of the drainage,but the water level difference gradually becomes smaller as time increases,and the prediction results of the three models tend to be consistent around 60 days.The MODFLOW model,the FEFLOW model,and the Subdomain-Analytic Element Method model took 36 minutes and 46 seconds,44 minutes and 15 seconds,and 15 minutes and 56 seconds to predict the dewatering rate of Ordovician limestone aquifer,respectively.Therefore,when dealing with moderately complex coal mine groundwater flow field problems such as dewatering rate prediction,the Subdomain-Analytic Element Method model has reliable simulation results and higher computational efficiency than MODFLOW model and FEFLOW model.Applying the Subdomain-Analytic Element Method to simulate flow field does not require meshing,but only needs to input parameters of the model and hydraulic elements(such as inner boundaries of flow field,outer boundaries of flow field,pumping(injection)wells,transient flow,etc.)to quickly model.When adjusting flow field’s boundaries or simulation accuracy,only the input parameters of the model need to be modified,instead of using discrete simulation methods such as finite difference or finite element,it is necessary to re-adjust the model mesh after adjusting the boundaries or accuracy.At the same time,since the complex potential functions of various hydraulic elements in the Subdomain-Analytic Element Method model are mostly analytical functions on the complex plane,the discharge potential functions of each hydraulic element in the model are all functions of the coordinates of each point in the flow field and time,so the solution of the model is an analytical solution,which has high accuracy but is difficult to deal with three-dimensional flow field problem.In addition,the Subdomain-Analytic Element Method model is solved by superimposing the solutions of various linear differential equations that satisfy the flow field conditions.The sparseness of the coefficient matrix of the model’s system of equations is weaker than that of finite difference or finite element model’s system of equations.With the increase of the complexity of flow field(such as the increase in the number of hydraulic elements in flow field,the increase in the number of aquifer layers,etc.),the sparseness of the coefficient matrix of the Subdomain-Analytic Element Method model’s system of equations will be greatly weakened,resulting in a multiplied increase in the computational complexity of the model.Therefore,the Subdomain-Analytic Element Method is a simulation method suitable for the two-dimensional groundwater flow field problem of coal mine with moderate complexity.This method has the advantages of rapid modeling,flexible model adjustment,high simulation accuracy and high computational efficiency.