CN115983097A - Fast inversion method of coal seam gas drainage characteristic parameters based on borehole drainage data - Google Patents
Fast inversion method of coal seam gas drainage characteristic parameters based on borehole drainage data Download PDFInfo
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技术领域Technical Field
本发明涉及一种煤层瓦斯抽采特征参数快速反演方法,具体为一种基于钻孔抽采数据的煤层瓦斯抽采特征参数快速反演方法,属于煤矿瓦斯抽采技术领域。The invention relates to a method for rapid inversion of coal seam gas extraction characteristic parameters, in particular to a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data, and belongs to the technical field of coal mine gas extraction.
背景技术Background Art
作为瓦斯资源化利用的基础和煤矿瓦斯灾害的治本性措施,煤层瓦斯的采前预抽一直是煤矿开采工作中必不可少的环节。在抽采过程中,瓦斯抽采基本参数是瓦斯抽采系统规划设计,瓦斯抽采效果评价和瓦斯抽采工程安全技术管理的基本科学依据。因此如何快速准确地获得瓦斯抽采参数具有重要意义。As the basis for gas resource utilization and the fundamental measure for coal mine gas disasters, pre-extraction of coal seam gas has always been an indispensable part of coal mining. In the extraction process, the basic parameters of gas extraction are the basic scientific basis for the planning and design of gas extraction systems, the evaluation of gas extraction effects, and the safety and technical management of gas extraction projects. Therefore, how to quickly and accurately obtain gas extraction parameters is of great significance.
然而目前行业内对于煤层瓦斯抽采特征参数的测定普遍存在操作复杂、耗时费力的问题,以煤层渗透率为例:目前行业内煤矿的煤层渗透率测量方式主要有实验室测量和现场测试两类方法。在实验室测量煤样渗透率中,由于完整煤样制备难度大、煤样在钻取的过程中易出现裂缝,以及煤体的各向异性特征等原因,导致煤层渗透率的测量结果较现场情况出现较大偏差,因此实验室很难模拟真实情况,只能进行定性的、规律性的研究。而在现场测定煤层渗透率时,目前国内主要采用钻孔瓦斯径向流量法,该渗透率测定方法探测效果较好,但是径向流量法仍然存在着测定周期长、待测参数复杂等缺点。However, the determination of coal seam gas extraction characteristic parameters in the industry is generally complicated, time-consuming and labor-intensive. Take coal seam permeability as an example: There are currently two main methods for measuring coal seam permeability in coal mines in the industry: laboratory measurement and field testing. In the laboratory measurement of coal sample permeability, due to the difficulty in preparing complete coal samples, cracks in coal samples during drilling, and the anisotropic characteristics of coal bodies, the measurement results of coal seam permeability are significantly different from the on-site situation. Therefore, it is difficult for the laboratory to simulate the actual situation and can only conduct qualitative and regular research. When measuring coal seam permeability on-site, the borehole gas radial flow method is currently used in China. This permeability determination method has a good detection effect, but the radial flow method still has disadvantages such as a long measurement cycle and complex parameters to be measured.
在煤层气抽采作业过程中,瓦斯抽采特征参数的动态变化特征是通过生产资料直接体现。而煤层气生产资料是煤矿施工现场第一手数据,具有较高的真实性和准确性。因此关于如何实现通过生产资料快速而准确地反求瓦斯抽采特征参数,为煤层气安全高效开采提供科学支撑的问题,有着较好的发展前景,需要进一步研究。During the coalbed methane extraction operation, the dynamic change characteristics of gas extraction characteristic parameters are directly reflected through production data. Coalbed methane production data is the first-hand data of coal mine construction site, with high authenticity and accuracy. Therefore, the problem of how to quickly and accurately reverse the gas extraction characteristic parameters through production data to provide scientific support for safe and efficient coalbed methane mining has a good development prospect and needs further research.
与一般研究所用的正向推导不同,根据结果或信息反推事件发生的过程或机制称为“反演”,其核心思想在于可观测参数推测研究对象内部源参数。目前有学者分析了煤层渗透率的复杂变化特点,建立了二维条件下的煤层瓦斯流动非耦合数学模型,并使用超松弛迭代法进行求解,最终实现了通过煤层瓦斯压力反演渗透率。但在实际施工过程中,煤层压力本身作为待测瓦斯抽采特征参数,测量往往存在操作复杂且具有滞后性的问题。还有学者建立了煤层双孔隙的耦合无量纲方程,并在此基础上提出了新的煤基质渗透率和裂隙渗透率的反演方法,结果表明基于流固耦合控制方程的反演算法具有较高的准确性。但是该研究只是通过试算匹配,并不涉及具体的非线性反演方法,具体应用效果较差。Different from the forward deduction used in general research, the process or mechanism of inferring the occurrence of an event based on the results or information is called "inversion", and its core idea is to infer the internal source parameters of the research object from observable parameters. At present, some scholars have analyzed the complex change characteristics of coal seam permeability, established a non-coupled mathematical model of coal seam gas flow under two-dimensional conditions, and used the super-relaxation iteration method to solve it, and finally realized the inversion of permeability through coal seam gas pressure. However, in the actual construction process, the coal seam pressure itself is used as a characteristic parameter of gas extraction to be measured, and the measurement often has the problem of complex operation and hysteresis. Other scholars have established a coupled dimensionless equation for the dual porosity of coal seams, and on this basis proposed a new inversion method for coal matrix permeability and fracture permeability. The results show that the inversion algorithm based on the fluid-solid coupling control equation has higher accuracy. However, this study only uses trial matching, and does not involve specific nonlinear inversion methods, and the specific application effect is poor.
因此,如何提供一种新的方法,使其以煤层多场耦合三维模型为基础,将煤层瓦斯抽采特征参数作为目标,搭建基于真实生产资料的煤层抽采特征参数反演算法,从而快速且精准的得出煤层抽采特征参数,是本行业的研究方向之一。Therefore, how to provide a new method based on the coal seam multi-field coupled three-dimensional model, take the coal seam gas extraction characteristic parameters as the target, and build a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately obtain the coal seam extraction characteristic parameters, is one of the research directions of this industry.
发明内容Summary of the invention
针对上述现有技术存在的问题,本发明提供一种基于钻孔抽采数据的煤层瓦斯抽采特征参数快速反演方法,其以煤层多场耦合三维模型为基础,将煤层瓦斯抽采特征参数作为目标,搭建基于真实生产资料的煤层抽采特征参数反演算法,从而快速且精准的得出煤层抽采特征参数。In response to the problems existing in the above-mentioned prior art, the present invention provides a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data. The method is based on a three-dimensional model of coal seam multi-field coupling, takes coal seam gas extraction characteristic parameters as the target, and builds a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately derive the coal seam extraction characteristic parameters.
为了实现上述目的,本发明采用的技术方案是:一种基于钻孔抽采数据的煤层瓦斯抽采特征参数快速反演方法,具体步骤为:In order to achieve the above purpose, the technical solution adopted by the present invention is: a method for rapid inversion of coal seam gas extraction characteristic parameters based on drilling extraction data, the specific steps are:
步骤一、根据瓦斯渗流理论,先建立煤层内瓦斯渗流数学模型,根据该数学模型能确定初始渗透率及钻孔抽采时间与煤层瓦斯压力之间的关系,然后确定煤层瓦斯流量与煤层瓦斯压力之间的关系式,将该关系式与建立的煤层内瓦斯渗流数学模型相结合,从而建成瓦斯流量正演模型,该瓦斯流量正演模型中所涉及的煤层物性参数以及边界条件根据现场地质情况确定,最后根据该瓦斯流量正演模型得出以煤层初始渗透率及抽采时间为自变量的正演瓦斯流量函数;Step 1: According to the gas seepage theory, a mathematical model of gas seepage in coal seams is first established. According to the mathematical model, the relationship between the initial permeability and the drilling extraction time and the coal seam gas pressure can be determined. Then, the relationship between the coal seam gas flow rate and the coal seam gas pressure is determined. The relationship is combined with the established mathematical model of gas seepage in coal seams to build a gas flow forward model. The coal seam physical parameters and boundary conditions involved in the gas flow forward model are determined according to the on-site geological conditions. Finally, according to the gas flow forward model, a forward gas flow function with the initial permeability of the coal seam and the extraction time as independent variables is obtained;
步骤二、通过瓦斯流量传感器采集现场瓦斯抽采流量,并将获得的抽采数据进行拟合形成连续函数,该连续函数即为拟合现场瓦斯抽采流量函数;Step 2: Collect the on-site gas extraction flow rate through a gas flow sensor, and fit the obtained extraction data to form a continuous function, which is the fitting on-site gas extraction flow rate function;
步骤三、将步骤一获得的正演瓦斯流量函数与步骤二获得的拟合现场瓦斯抽采流量函数,两者之间的差函数D(k0,t)作为适应度函数,并以适应度函数最小值为目标;Step 3: The difference function D(k 0 ,t) between the forward modeling gas flow function obtained in
步骤四、采用粒子群算法寻找使步骤三中适应度函数最小值时对应的煤层初始渗透率和钻孔抽采时间;Step 4: Use the particle swarm algorithm to find the initial permeability of the coal seam and the drilling and extraction time corresponding to the minimum value of the fitness function in
步骤五、通过步骤四获得的煤层初始渗透率及钻孔抽采时间,将该数据代入步骤一建立的瓦斯流量正演模型,最终根据该模型计算确定煤层的瓦斯抽采特征参数。Step 5: Substitute the initial permeability of the coal seam and the drilling extraction time obtained in
进一步,所述步骤一具体为:Further, the
A):根据瓦斯渗流理论,建立如式(1)所示瓦斯渗流三维流固耦合数学模型:A): According to the gas seepage theory, a three-dimensional fluid-solid coupling mathematical model of gas seepage is established as shown in formula (1):
式中,G代表煤的剪切模量,MPa,G=E/2(1+v);K和E分别为煤的体积模量和杨氏模量,MPa,K=E/3(1-2v);v代表煤的泊松比;α是煤的Biot系数,α=1-K/KS;εs为煤的吸附诱导体积应变;εL是朗缪尔体积应变常量;S=εv+(P/Ks)-εs,S0=(p0/Ks)-εLp0/(p0+pL);p0代表煤层初始压力;p代表煤层瓦斯压力;φ0代表煤层初始孔隙度;φ表示煤层孔隙度,k表示煤层渗透率, k0表示煤层初始渗透率;In the formula, G represents the shear modulus of coal, MPa, G = E/2(1+v); K and E are the bulk modulus and Young's modulus of coal, respectively, MPa, K = E/3(1-2v); v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α = 1-K/K S ; ε s is the adsorption-induced volume strain of coal; ε L is the Langmuir volume strain constant; S = ε v +(P/K s )-ε s , S 0 =(p 0 /K s )-ε L p 0 /(p 0 +p L ); p 0 represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ 0 represents the initial porosity of the coal seam; φ represents the porosity of the coal seam, k represents the permeability of the coal seam, k 0 represents the initial permeability of the coal seam;
B):求解式(1)能得到在煤层初始渗透率k0下任意时刻瓦斯压力分布,并依此得到此时煤层内单位体积煤体瓦斯含量m,如式(2)所示:B): Solving equation (1) can obtain the gas pressure distribution at any time under the initial permeability k0 of the coal seam, and based on this, the gas content m per unit volume of the coal body in the coal seam at this time can be obtained, as shown in equation (2):
其中,ρa为标准状态下瓦斯密度,kg/m3;ρc是煤密度,kg/m3;VL为朗缪尔体积常数,m3/kg;PL代表朗缪尔压力常数,MPa;Wherein, ρa is the gas density under standard conditions, kg/m 3 ; ρc is the coal density, kg/m 3 ; VL is the Langmuir volume constant, m 3 /kg; PL represents the Langmuir pressure constant, MPa;
将抽采t时刻单位体积煤体内瓦斯量m|t对煤体积分,能得到任意体积煤体瓦斯含量M|t,如式(3)所示:By dividing the gas content m| t per unit volume of coal at extraction time t by the coal volume, the gas content M| t of any volume of coal can be obtained, as shown in formula (3):
M|t=∫∫∫Vm|tdx dy dz (3)M| t =∫∫∫ V m| t dx dy dz (3)
式中:M|t为t时刻煤层内的瓦斯含量,kg。Where: M| t is the gas content in the coal seam at time t, kg.
C):任意t时刻瓦斯抽采的流量可以表示为:C): The gas extraction flow rate at any time t can be expressed as:
式中,Q|t为t时刻的瓦斯抽采流量,m3/s;Where, Q| t is the gas extraction flow rate at time t, m 3 /s;
由式(1)到式(4)得到,瓦斯抽采流量Q为初始渗透率k0和抽采时间t的函数,即From equations (1) to (4), we can see that the gas drainage flow rate Q is a function of the initial permeability k0 and the drainage time t, that is,
Q=Q(k0,t) (5)Q=Q(k 0 ,t) (5)
通过步骤A)-C)能建立抽采瓦斯流量与煤层初始渗透率及钻孔抽采时间之间的关系,即瓦斯流量正演模型,在瓦斯流量正演模型中通过任意给定煤层初始渗透率k0和抽采时间t能得到该时刻的钻孔瓦斯流量。Through steps A)-C), the relationship between the extracted gas flow rate and the initial permeability of the coal seam and the drilling extraction time, that is, the gas flow forward model, can be established. In the gas flow forward model, the borehole gas flow rate at that moment can be obtained by any given coal seam initial permeability k0 and extraction time t.
进一步,所述步骤二中拟合现场瓦斯抽采流量函数具体为:Furthermore, the function of fitting the on-site gas extraction flow rate in
式中,t表示抽采时间,d;t0表示首次记录瓦斯流量时钻孔已抽采时间,d;QR为拟合现场瓦斯抽采流量,m3/min;a、b代表函数系数。Where, t represents the extraction time, d; t0 represents the extraction time of the borehole when the gas flow is first recorded, d; QR is the fitted on-site gas extraction flow, m3 /min; a and b represent function coefficients.
进一步,所述步骤三中差函数D(k0,t)具体为:Furthermore, the difference function D(k 0 ,t) in
式中,下标i=1,2……n,表示监测的数据时间点;In the formula, subscript i = 1, 2, ..., n, represents the time point of the monitored data;
上式中D(k0,t)值越小,表明反演所得的煤层初始渗透率k0和抽采时间t越接近实际值,故以该函数获取最小值为目标。In the above formula, the smaller the value of D(k 0 ,t) is, the closer the initial permeability k 0 and extraction time t of the coal seam obtained by inversion are to the actual values. Therefore, the goal is to obtain the minimum value of this function.
进一步,所述步骤四的具体过程为:Further, the specific process of
①预设粒子群算法的参数:设定算法中种群包含的个体总数N,最大迭代次数ger,粒子运动的最大速度Vmax和最小速度Vmin,个体学习因子c1,社会学习因子c2,惯性因子w,截断误差C;① Preset the parameters of the particle swarm algorithm: set the total number of individuals N contained in the population of the algorithm, the maximum number of iterations ger, the maximum speed V max and minimum speed V min of particle movement, the individual learning factor c 1 , the social learning factor c 2 , the inertia factor w, and the truncation error C;
②确定反演区间边界,并在反演区间内随机生成N个粒子,第i个粒子的初始位置Xi以及粒子变化区间分别如式(7)和式(8)所示:② Determine the inversion interval boundary and randomly generate N particles in the inversion interval. The initial position Xi of the i-th particle and the particle change interval are shown in equations (7) and (8) respectively:
Xi=(k0it) (7) Xi =( k0it ) (7)
U≤Xi≤T (8)U≤X i ≤T (8)
其中,i=(1,2,3...N),U,T分别代表粒子的渗透率下限和上限;Where i = (1, 2, 3...N), U and T represent the lower and upper limits of the permeability of the particles, respectively;
根据适应度函数D(k0,t)计算当前粒子位置适应度,比较各粒子适应度后记录种群历史最佳位置Gb_X和此时的种群历史最佳适应度Gb,并初始化粒子群历史最佳位置Pb_X=X;Calculate the fitness of the current particle position according to the fitness function D(k 0 ,t), compare the fitness of each particle, record the population's historical best position Gb_X and the population's historical best fitness Gb at this time, and initialize the particle group's historical best position Pb_X=X;
③开始迭代,更新粒子群位置,第i个粒子的位置更新公式如式(9)所示:③ Start iteration and update the position of the particle swarm. The position update formula of the i-th particle is shown in formula (9):
其中,L为当前迭代次数,表示粒子移动速度,使用式(10)表示Where L is the current iteration number, represents the particle moving speed, which can be expressed using formula (10):
其中粒子惯性因子w,代表粒子具有向自身固有运动方向移动的趋势;个体学习因子c1和社会学习因子c2分别赋予粒子个体记忆属性和社会属性,代表粒子有向自身历史最佳位置和种群历史最佳位置靠拢的趋势;r1,r2是两个独立的随机参数,使粒子的运动更具随机性,增大了全局寻优的可能性;The particle inertia factor w represents the tendency of the particle to move in its inherent direction of motion; the individual learning factor c1 and the social learning factor c2 respectively give the particle individual memory attributes and social attributes, representing the tendency of the particle to move toward its own historical best position and the population historical best position; r1 and r2 are two independent random parameters, which make the particle movement more random and increase the possibility of global optimization;
为了避免粒子在寻优过程中步幅过大略过最优位置,因此对粒子的速度vi进行限制:In order to prevent the particle from skipping the optimal position due to excessive strides during the optimization process, the particle velocity v i is limited:
Vmin<=vi<=Vmax (11)V min <= vi <= V max (11)
其中,Vmin,Vmax分别代表粒子速度下限和上限,即每次迭代过程中渗透率的变化范围;Among them, V min and V max represent the lower and upper limits of particle velocity, respectively, that is, the range of permeability change during each iteration;
④比较当前煤层初始渗透率及抽采时间下的瓦斯流量匹配程度并更新Gb_X,Gb,Pb_X;④ Compare the gas flow matching degree under the current coal seam initial permeability and extraction time and update Gb_X, Gb, Pb_X;
⑤判断是否满足终止条件,若满足则跳出迭代,输出适应度函数最小值时对应的煤层初始渗透率和钻孔抽采时间,否则回到步骤③继续迭代计算。⑤ Determine whether the termination condition is met. If so, exit the iteration and output the initial permeability of the coal seam and the drilling extraction time corresponding to the minimum value of the fitness function. Otherwise, return to
进一步,所述步骤五中煤层的瓦斯抽采特征参数包括煤层瓦斯压力p、剩余煤层瓦斯含量M、瓦斯抽采率η、煤层渗透率k及有效抽采半径r;其中煤层瓦斯压力p、剩余煤层瓦斯含量M、煤层渗透率k通过瓦斯流量正演模型求解获得,瓦斯抽采率η由煤层剩余瓦斯量M与煤层初始瓦斯含量M0比值得到,有效抽采半径r设定为残余煤层瓦斯压力低于0.74MPa的区域。Furthermore, the gas extraction characteristic parameters of the coal seam in step five include coal seam gas pressure p, remaining coal seam gas content M, gas extraction rate η, coal seam permeability k and effective extraction radius r; wherein the coal seam gas pressure p, remaining coal seam gas content M, and coal seam permeability k are obtained by solving the gas flow forward model, the gas extraction rate η is obtained by the ratio of the remaining coal seam gas amount M to the initial coal seam gas content M0 , and the effective extraction radius r is set to the area where the residual coal seam gas pressure is lower than 0.74MPa.
进一步,所述粒子惯性因子w为随迭代次数变化的变量,如式(12)所示:Furthermore, the particle inertia factor w is a variable that changes with the number of iterations, as shown in formula (12):
w=w_1-(w_1-w_2)*L/ger (12)w=w_1-(w_1-w_2)*L/ger (12)
其中,w_1和w_2分别代表惯性系数的上限和下限,L为当前迭代次数,ger为最大迭代次数;迭代前期惯性因子w较大,粒子以较大飞行速度在变量空间移动,更易于发现全局最优值;迭代后期惯性因子w较小,使算法的收敛性大大提高。Among them, w_1 and w_2 represent the upper and lower limits of the inertia coefficient respectively, L is the current number of iterations, and ger is the maximum number of iterations; in the early stage of iteration, the inertia factor w is larger, and the particles move in the variable space at a higher flying speed, which makes it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, which greatly improves the convergence of the algorithm.
进一步,所述步骤⑤中的终止条件为:循环达到最大迭代次数,或者在连续三次迭代过程中适应度函数D(k0,t)的变化小于设定的截断误差C。Furthermore, the termination condition in
与现有技术相比,本发明先建立煤层内瓦斯渗流数学模型,并结合瓦斯抽采流量演化特征与瓦斯压力分布特征的参数表征关系,建成瓦斯流量正演模型,该瓦斯流量正演模型中所涉及的煤层物性参数以及边界条件根据现场地质情况确定,通过正演模型得出;接着采集现场瓦斯抽采数据拟合成连续函数,作为现场瓦斯抽采流量函数;将上述正演瓦斯流量函数和现场拟合的瓦斯抽采流量函数作差,形成的差函数作为适应度函数;采用粒子群算法寻找适应度函数最小值时对应的煤层初始渗透率和钻孔抽采时间;最后将获得的煤层初始渗透率及钻孔抽采时间代入上述瓦斯流量正演模型,计算确定煤层的瓦斯抽采特征参数。因此本发明能以煤层多场耦合三维模型为基础,将煤层瓦斯抽采特征参数作为目标,搭建基于真实生产资料的煤层抽采特征参数反演算法,从而快速且精准的得出煤层抽采特征参数。Compared with the prior art, the present invention first establishes a mathematical model of gas seepage in the coal seam, and combines the parameter characterization relationship between the gas extraction flow evolution characteristics and the gas pressure distribution characteristics to build a gas flow forward model. The coal seam physical parameters and boundary conditions involved in the gas flow forward model are determined according to the on-site geological conditions and obtained through the forward model; then the on-site gas extraction data are collected and fitted into a continuous function as the on-site gas extraction flow function; the above forward gas flow function and the on-site fitted gas extraction flow function are subtracted, and the difference function formed is used as the fitness function; the particle swarm algorithm is used to find the initial permeability and drilling extraction time of the coal seam corresponding to the minimum value of the fitness function; finally, the obtained initial permeability and drilling extraction time of the coal seam are substituted into the above gas flow forward model to calculate and determine the gas extraction characteristic parameters of the coal seam. Therefore, the present invention can be based on the coal seam multi-field coupling three-dimensional model, take the coal seam gas extraction characteristic parameters as the target, and build a coal seam extraction characteristic parameter inversion algorithm based on real production data, so as to quickly and accurately obtain the coal seam extraction characteristic parameters.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本发明整体的反演流程图;FIG1 is an overall inversion flow chart of the present invention;
图2是本发明中采用粒子群算法寻找适应度函数最小值的流程图;FIG2 is a flow chart of using a particle swarm algorithm to find the minimum value of a fitness function in the present invention;
图3是本发明实施例中煤层几何参数和边界条件图;FIG3 is a diagram of coal seam geometric parameters and boundary conditions in an embodiment of the present invention;
图4是本发明实施例中煤层初始渗透率及抽采时间反演结果图;FIG4 is a graph showing the inversion results of the initial permeability of the coal seam and the extraction time in an embodiment of the present invention;
图5是本发明实施例中抽采94天时煤层瓦斯压力分布图;FIG5 is a diagram showing the distribution of coal seam gas pressure after 94 days of extraction in an embodiment of the present invention;
图6是本发明实施例中抽采94天时有效抽采半径图;FIG6 is a diagram of the effective extraction radius when extraction is performed for 94 days in an embodiment of the present invention;
图中,空白区域代表有效半径影响范围;In the figure, the blank area represents the effective radius influence range;
图7是本发明实施例中抽采94天时煤层剩余瓦斯分布示意图;FIG7 is a schematic diagram of the distribution of residual gas in the coal seam after 94 days of extraction in an embodiment of the present invention;
图8是本发明实施例中抽采94天时煤层渗透率分布图。FIG8 is a coal seam permeability distribution diagram after 94 days of extraction in an embodiment of the present invention.
具体实施方式DETAILED DESCRIPTION
下面将对本发明作进一步说明。The present invention will be further described below.
如图1所示,本发明的具体步骤为:As shown in Figure 1, the specific steps of the present invention are:
步骤一、建立瓦斯流量正演模型:Step 1: Establish a gas flow forward model:
A):根据瓦斯渗流理论,建立如式(1)所示瓦斯渗流三维流固耦合数学模型:A): According to the gas seepage theory, a three-dimensional fluid-solid coupling mathematical model of gas seepage is established as shown in formula (1):
式中,G代表煤的剪切模量,MPa,G=E/2(1+v);K和E分别为煤的体积模量和杨氏模量,MPa,K=E/3(1-2v);v代表煤的泊松比;α是煤的Biot系数,α=1-K/KS;εs为煤的吸附诱导体积应变;εL是朗缪尔体积应变常量;S=εv+(P/Ks)-εs,S0=(p0/Ks)-εLp0/(p0+pL);p0代表煤层初始压力;p代表煤层瓦斯压力;φ0代表煤层初始孔隙度;φ表示煤层孔隙度,k表示煤层渗透率, k0表示煤层初始渗透率;In the formula, G represents the shear modulus of coal, MPa, G = E/2(1+v); K and E are the bulk modulus and Young's modulus of coal, respectively, MPa, K = E/3(1-2v); v represents the Poisson's ratio of coal; α is the Biot coefficient of coal, α = 1-K/K S ; ε s is the adsorption-induced volume strain of coal; ε L is the Langmuir volume strain constant; S = ε v +(P/K s )-ε s , S 0 =(p 0 /K s )-ε L p 0 /(p 0 +p L ); p 0 represents the initial pressure of the coal seam; p represents the gas pressure of the coal seam; φ 0 represents the initial porosity of the coal seam; φ represents the porosity of the coal seam, k represents the permeability of the coal seam, k 0 represents the initial permeability of the coal seam;
B):求解式(1)能得到在煤层初始渗透率k0下任意时刻瓦斯压力分布,并依此得到此时煤层内单位体积煤体瓦斯含量m,如式(2)所示:B): Solving equation (1) can obtain the gas pressure distribution at any time under the initial permeability k0 of the coal seam, and based on this, the gas content m per unit volume of the coal body in the coal seam at this time can be obtained, as shown in equation (2):
其中,ρa为标准状态下瓦斯密度,kg/m3;ρc是煤密度,kg/m3;VL为朗缪尔体积常数,m3/kg;PL代表朗缪尔压力常数,MPa;Wherein, ρa is the gas density under standard conditions, kg/m 3 ; ρc is the coal density, kg/m 3 ; VL is the Langmuir volume constant, m 3 /kg; PL represents the Langmuir pressure constant, MPa;
将抽采t时刻单位体积煤体内瓦斯量m|t对煤体积分,能得到任意体积煤体瓦斯含量M|t,如式(3)所示:By dividing the gas content m| t per unit volume of coal at extraction time t by the coal volume, the gas content M| t of any volume of coal can be obtained, as shown in formula (3):
M|t=∫∫∫Vm|tdx dy dz (3)M| t =∫∫∫ V m| t dx dy dz (3)
式中:M|t为t时刻煤层内的瓦斯含量,kg。Where: M| t is the gas content in the coal seam at time t, kg.
C):任意t时刻瓦斯抽采的流量可以表示为:C): The gas extraction flow rate at any time t can be expressed as:
式中,Q|t为t时刻的瓦斯抽采流量,m3/s;Where, Q| t is the gas extraction flow rate at time t, m 3 /s;
由式(1)到式(4)得到,瓦斯抽采流量Q为初始渗透率k0和抽采时间t的函数,即From equations (1) to (4), we can see that the gas drainage flow rate Q is a function of the initial permeability k0 and the drainage time t, that is,
Q=Q(k0,t) (5)Q=Q(k 0 ,t) (5)
通过步骤A)-C)能建立抽采瓦斯流量与煤层初始渗透率及钻孔抽采时间之间的关系,即瓦斯流量正演模型,在瓦斯流量正演模型中通过任意给定煤层初始渗透率k0和抽采时间t能得到该时刻的钻孔瓦斯流量。Through steps A)-C), the relationship between the extracted gas flow rate and the initial permeability of the coal seam and the drilling extraction time, that is, the gas flow forward model, can be established. In the gas flow forward model, the borehole gas flow rate at that moment can be obtained by any given coal seam initial permeability k0 and extraction time t.
步骤二、通过瓦斯流量传感器采集现场瓦斯抽采流量,并将获得的抽采数据进行拟合形成连续函数,该连续函数即为拟合现场瓦斯抽采流量函数,其中拟合现场瓦斯抽采流量函数具体为:Step 2: Collect the on-site gas extraction flow rate through the gas flow sensor, and fit the obtained extraction data to form a continuous function, which is the fitting on-site gas extraction flow rate function, wherein the fitting on-site gas extraction flow rate function is specifically:
式中,t表示抽采时间,d;t0表示首次记录瓦斯流量时钻孔已抽采时间,d;QR为拟合现场瓦斯抽采流量,m3/min;a、b代表函数系数。Where, t represents the extraction time, d; t0 represents the extraction time of the borehole when the gas flow is first recorded, d; QR is the fitted on-site gas extraction flow, m3 /min; a and b represent function coefficients.
步骤三、将步骤一获得的正演瓦斯流量函数与步骤二获得的拟合现场瓦斯抽采流量函数,两者之间的差函数D(k0,t)作为适应度函数,其中差函数D(k0,t)具体为:Step 3: The difference function D(k 0 , t) between the forward modeling gas flow function obtained in
式中,下标i=1,2……n,表示监测的数据时间点;In the formula, subscript i = 1, 2, ..., n, represents the time point of the monitored data;
上式中D(k0,t)值越小,表明反演的煤层初始渗透率k0和抽采时间t越接近实际值,故以该函数获取最小值为目标。In the above formula, the smaller the value of D(k 0 ,t) is, the closer the inverted initial permeability k 0 of the coal seam and the extraction time t are to the actual values. Therefore, the goal is to obtain the minimum value of this function.
步骤四、采用粒子群算法寻找使步骤三中适应度函数最小值时对应的煤层初始渗透率和钻孔抽采时间,具体过程为:Step 4: Use the particle swarm algorithm to find the initial permeability of the coal seam and the drilling and extraction time corresponding to the minimum value of the fitness function in
①预设粒子群算法的参数:设定算法中种群包含的个体总数N,最大迭代次数ger,粒子运动的最大速度Vmax和最小速度Vmin,个体学习因子c1,社会学习因子c2,惯性因子w,截断误差C;① Preset the parameters of the particle swarm algorithm: set the total number of individuals N contained in the population of the algorithm, the maximum number of iterations ger, the maximum speed V max and minimum speed V min of particle movement, the individual learning factor c1, the social learning factor c2, the inertia factor w, and the truncation error C;
②确定反演区间边界,并在反演区间内随机生成N个粒子,第i个粒子的初始位置Xi以及粒子变化区间分别如式(7)和式(8)所示:② Determine the inversion interval boundary and randomly generate N particles in the inversion interval. The initial position Xi of the i-th particle and the particle change interval are shown in equations (7) and (8) respectively:
Xi=(k0it) (7) Xi =( k0it ) (7)
U≤Xi≤T (8)U≤X i ≤T (8)
其中,i=(1,2,3...N),U,T分别代表粒子的渗透率下限和上限;Where i = (1, 2, 3...N), U and T represent the lower and upper limits of the permeability of the particles, respectively;
根据适应度函数D(k0,t)计算当前粒子位置适应度,比较各粒子适应度后记录种群历史最佳位置Gb_X和此时的种群历史最佳适应度Gb,并初始化粒子群历史最佳位置Pb_X=X;Calculate the fitness of the current particle position according to the fitness function D(k 0 ,t), compare the fitness of each particle, record the population's historical best position Gb_X and the population's historical best fitness Gb at this time, and initialize the particle group's historical best position Pb_X=X;
③开始迭代,更新粒子群位置,第i个粒子的位置更新公式如式(9)所示:③ Start iteration and update the position of the particle swarm. The position update formula of the i-th particle is shown in formula (9):
其中,L为当前迭代次数,表示粒子移动速度,使用式(10)表示Where L is the current iteration number, represents the particle moving speed, which can be expressed using formula (10):
其中粒子惯性因子w,代表粒子具有向自身固有运动方向移动的趋势;个体学习因子c1和社会学习因子c2分别赋予粒子个体记忆属性和社会属性,代表粒子有向自身历史最佳位置和种群历史最佳位置靠拢的趋势;r1,r2是两个独立的随机参数,使粒子的运动更具随机性,增大了全局寻优的可能性;The particle inertia factor w represents the tendency of the particle to move in its inherent direction of motion; the individual learning factor c1 and the social learning factor c2 respectively give the particle individual memory attributes and social attributes, representing the tendency of the particle to move toward its own historical best position and the population historical best position; r1 and r2 are two independent random parameters, which make the particle movement more random and increase the possibility of global optimization;
上述粒子群算法不设变异过程,容易陷入局部的最优解中,最终无法收敛到全局的最优位置,因此将速度公式中的粒子惯性因子w由固定值更改为随迭代次数变化的变量,即粒子惯性因子w为随迭代次数变化的变量,如式(11)所示:The above particle swarm algorithm does not set a mutation process and is prone to fall into a local optimal solution and ultimately cannot converge to the global optimal position. Therefore, the particle inertia factor w in the velocity formula is changed from a fixed value to a variable that changes with the number of iterations, that is, the particle inertia factor w is a variable that changes with the number of iterations, as shown in formula (11):
w=w_1-(w_1-w_2)*L/ger (11)w=w_1-(w_1-w_2)*L/ger (11)
其中,w_1和w_2分别代表惯性系数的上限和下限,L为当前迭代次数,ger为最大迭代次数;迭代前期惯性因子w较大,粒子以较大飞行速度在变量空间移动,更易于发现全局最优值;迭代后期惯性因子w较小,使算法的收敛性大大提高。Among them, w_1 and w_2 represent the upper and lower limits of the inertia coefficient respectively, L is the current number of iterations, and ger is the maximum number of iterations; in the early stage of iteration, the inertia factor w is larger, and the particles move in the variable space at a higher flying speed, which makes it easier to find the global optimal value; in the later stage of iteration, the inertia factor w is smaller, which greatly improves the convergence of the algorithm.
为了避免粒子在寻优过程中步幅过大略过最优位置,因此对粒子的速度vi进行限制:In order to prevent the particle from skipping the optimal position due to excessive strides during the optimization process, the particle velocity v i is limited:
Vmin<=vi<=Vmax (12)V min <= vi <= V max (12)
其中,Vmin,Vmax分别代表粒子速度下限和上限,即每次迭代过程中渗透率的变化范围;Among them, V min and V max represent the lower and upper limits of particle velocity, respectively, that is, the range of permeability change during each iteration;
④比较当前煤层初始渗透率及抽采时间下的瓦斯流量匹配程度并更新Gb_X,Gb,Pb_X;④ Compare the gas flow matching degree under the current coal seam initial permeability and extraction time and update Gb_X, Gb, Pb_X;
⑤判断是否满足终止条件,所述终止条件为:循环达到最大迭代次数,或者在连续三次迭代过程中适应度函数D(k0,t)的变化小于设定的截断误差C;若满足则跳出迭代,输出适应度函数最小值时对应的煤层初始渗透率和钻孔抽采时间,否则回到步骤③继续迭代计算。⑤ Determine whether the termination condition is met, which is: the cycle reaches the maximum number of iterations, or the change of the fitness function D(k 0 ,t) is less than the set truncation error C during three consecutive iterations; if it is met, the iteration is jumped out, and the initial permeability of the coal seam and the drilling and extraction time corresponding to the minimum value of the fitness function are output, otherwise return to step ③ to continue the iterative calculation.
步骤五、通过步骤四获得的煤层初始渗透率及钻孔抽采时间,将该数据代入步骤一建立的瓦斯流量正演模型,最终根据该模型计算确定煤层的瓦斯抽采特征参数,其中煤层的瓦斯抽采特征参数包括煤层瓦斯压力p、剩余煤层瓦斯含量M、瓦斯抽采率η、煤层渗透率k及有效抽采半径r;其中煤层瓦斯压力p、剩余煤层瓦斯含量M、煤层渗透率k通过瓦斯流量正演模型求解获得,瓦斯抽采率η由煤层剩余瓦斯量M与煤层初始瓦斯含量M0比值得到,有效抽采半径r设定为残余煤层瓦斯压力低于0.74MPa的区域。
试验证明:Tests prove:
为了验证采用本发明反演获得煤层的瓦斯抽采特征参数的具体过程,采用实际煤矿进行模拟验证:选取平煤十矿(戊8.9-20230机巷)第125组1#钻孔为研讨对象,以煤层初始渗透率及首次记录钻孔流量时钻孔抽采时间为反演目标采用本发明进行反演。由于本发明中瓦斯流量正演模型由一系列偏微分方程组成,可借助COMSOL with MATLAB平台解算。确定煤层几何参数和边界条件如图3所示,物性参数如表1所示:In order to verify the specific process of obtaining the gas extraction characteristic parameters of the coal seam by inversion using the present invention, a simulation verification was carried out using an actual coal mine: the 1# borehole of the 125th group of Pingmei Tenth Mine (E 8.9-20230 machine lane) was selected as the research object, and the initial permeability of the coal seam and the drilling extraction time when the drilling flow was first recorded were used as the inversion targets to perform inversion using the present invention. Since the gas flow forward model in the present invention is composed of a series of partial differential equations, it can be solved with the help of the COMSOL with MATLAB platform. The geometric parameters and boundary conditions of the coal seam are determined as shown in Figure 3, and the physical parameters are shown in Table 1:
表1煤层物性参数表Table 1 Coal seam physical properties parameters
瓦斯抽采模拟初始条件为:The initial conditions for gas extraction simulation are:
在t=0时刻,煤岩体内瓦斯初始压力为2MPa,边界位移量为0,即:At t=0, the initial gas pressure in the coal rock mass is 2MPa, and the boundary displacement is 0, that is:
式中,p|t=0和u|t=0分别代表初始时刻模型内瓦斯压力(MPa)和位移值(m)。Where p| t=0 and u| t=0 represent the gas pressure (MPa) and displacement value (m) in the model at the initial moment, respectively.
瓦斯抽采模拟边界条件为:The boundary conditions for gas extraction simulation are:
①渗流边界条件:模型外表面边界以及钻孔封孔段壁面设置无流动边界条件,抽采段按抽采负压设置定压力边界,即① Seepage boundary conditions: The model outer surface boundary and the borehole sealing section wall are set with no flow boundary conditions, and the extraction section is set with a fixed pressure boundary according to the extraction negative pressure, that is,
式中,n·v|外边界和n·v|钻孔封孔段分别表示通过模型外边界和钻孔封孔段的单位面积气体流量(kg/(s·m2));p|钻孔抽采段表示钻孔抽采段的边界压力,MPa。Where n·v| outer boundary and n·v| borehole sealing section represent the gas flow rate per unit area through the model outer boundary and borehole sealing section, respectively (kg/(s·m 2 )); p| borehole extraction section represents the boundary pressure of the borehole extraction section, MPa.
②煤体变形边界条件:根据煤层埋深情况,在上表面施加8MPa的均匀载荷模拟上层煤岩体自重,底面以及钻孔封孔段设置固定约束边界,侧边界设置法向约束边界,抽采段设置自由变形边界,即:② Coal deformation boundary conditions: According to the buried depth of the coal seam, a uniform load of 8MPa is applied on the upper surface to simulate the deadweight of the upper coal and rock mass. Fixed constraint boundaries are set on the bottom surface and the borehole sealing section, normal constraint boundaries are set on the side boundaries, and free deformation boundaries are set on the extraction section, that is:
式中,-σijnj|上表面表示模型上表面所受载荷(MPa);u|底面和u|钻孔封孔段分别表示模型底面以及钻孔封孔段变形位移(m);u·n|侧边界表示模型侧面法向位移(m)。Where -σ ij n j | upper surface represents the load on the upper surface of the model (MPa); u| bottom surface and u| drilling and sealing section represent the deformation displacement of the bottom surface of the model and the drilling and sealing section respectively (m); u·n| side boundary represents the normal displacement of the side surface of the model (m).
对现场瓦斯抽采流量数据按式(5)所示形式进行拟合,结果为:The on-site gas extraction flow data is fitted according to the form shown in formula (5), and the result is:
粒子群算法参数初始化数据由实际地质参数设置,煤层初始渗透率k0范围为(1×10-20,1×10-16),速度限制区间取初始渗透率范围10%,即(-5×10-18,5×10-18);设置粒子个数N为50个,最大迭代次数ger为100次,截断误差0.001,个体学习因子c1取2,社会学习因子c2取2。The parameter initialization data of the particle swarm algorithm is set by the actual geological parameters. The initial permeability k0 of the coal seam is in the range of (1× 10-20 , 1× 10-16 ), and the velocity limit interval is 10% of the initial permeability range, that is, (-5× 10-18 , 5× 10-18 ); the number of particles N is set to 50, the maximum number of iterations ger is 100 times, the truncation error is 0.001, the individual learning factor c1 is 2, and the social learning factor c2 is 2.
最终反演结果如图4至图8所示;其中图4为煤层初始渗透率及钻孔抽采时间反演结果图,从图中可以看出反演所得初始渗透率为3.79×10-17m2,钻孔抽采时间为94天。进一步以反演所得煤层初始渗透和钻孔抽采时间为基础推算煤层抽采参数演化情况。根据瓦斯流量正演模型,抽采第94天时煤层瓦斯压力分布如图5所示,此时煤层内瓦斯有效压力半径以及煤层剩余瓦斯含量分布分别如图6和图7所示,对全煤体积进行积分即可得到此时的煤层剩余瓦斯量为3321.8kg,瓦斯抽采率为61.6%,图8为抽采第94天时煤层中渗透率分布图。然后将上述反演得到的煤层抽采特征参数数据与该煤矿的实际数据进行比对得出,本发明的反演方法能快速且精准的获得煤层抽采特征参数。The final inversion results are shown in Figures 4 to 8; Figure 4 is the inversion result diagram of the initial permeability of the coal seam and the drilling extraction time. It can be seen from the figure that the initial permeability obtained by inversion is 3.79× 10-17 m2 , and the drilling extraction time is 94 days. The evolution of coal seam extraction parameters is further estimated based on the initial permeability and drilling extraction time of the coal seam obtained by inversion. According to the gas flow forward model, the gas pressure distribution of the coal seam on the 94th day of extraction is shown in Figure 5. At this time, the effective gas pressure radius in the coal seam and the distribution of the remaining gas content in the coal seam are shown in Figures 6 and 7 respectively. By integrating the total coal volume, the remaining gas amount in the coal seam at this time is 3321.8kg, and the gas extraction rate is 61.6%. Figure 8 is a permeability distribution diagram in the coal seam on the 94th day of extraction. Then the coal seam extraction characteristic parameter data obtained by the above inversion is compared with the actual data of the coal mine. The inversion method of the present invention can quickly and accurately obtain the coal seam extraction characteristic parameters.
以上所述仅是本发明的优选实施方式,应当指出:对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下,还可以做出若干改进和润饰,这些改进和润饰也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.
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