煤层气羽状水平井数值模拟模型的交替隐式算法

Alternating Direction Implicit(ADI) Algorithm in CBM Pinnate Horizontal Well Numerical Simulation Modeling

煤层气开采过程中通常采用数值模拟方法进行生产指标预测,其中的数值模型普遍采用三维全隐式差分法求解,模型涉及的参数变量多,求解难度大,计算复杂。根据煤层气的储气特征、吸附特征和解吸机理建立了反映煤层气解吸、扩散及渗流过程的气、水两相流动煤层气羽状水平井三维数学模型,模型考虑了煤层非均质各向异性的影响,运用块中心差分格式,对气、水相偏微分方程进行空间差分和时间差分,采用交替隐式(ADI)法求解,实现了煤层气羽状水平井开发数值模拟计算。交替方向格式可以把二维问题转化成一维问题,对x,y两个方向的迭代矩阵均为三对角矩阵,结构相同,易于编程计算。所建立的差分格式具有计算量小,稳定性好等优点,数值试验的结果表明效果良好。

The numerical simulation is an effective method to confirm CBM exploitation scheme and evaluate recovery factor. Present widely used 3D full implicit difference method is hard to compute and get solution. According to CBM storage and adsorption character-istics, as well as desorption mechanisms have modeled gas, water two phases flow CBM pinnate horizontal well 3D mathematical model can reflect CBM desorption, diffusion and seepage processes. The model has considered impacts from anisotropic coal seams, using block-centered finite difference scheme carried out spatial and temporal differences on gas, water phases partial differential equation, through ADI to get solution, realized CBM pinnate horizontal well exploitation numerical simulation computing. The alternating direc-tion scheme can transform two-dimensional problem into one-dimensional problem, to x, y two direction iterative matrixes are all tri-diagonal matrixes with same configuration, thus easy to programming computation. The difference scheme established has advantages of small computation amount and good stability;the results of numerical experimentation have shown good effect.