水平单裂隙介质井流分数阶模型及其解

摘要

为了计算裂隙介质井流问题的渗透系数张量，基于水平单裂隙介质含水层渗流有各向异性的特性，利用分数阶微分方程理论建立了水平单裂隙介质径向各向异性非稳定完整井流问题的时间分数阶（1／2阶）数学模型。通过特殊函数、分数阶导数和函数的 Laplace 变换和 Fourier 的定义及性质求出水平单裂隙介质径向各向异性非稳定完整井流模型的解析解。最后通过降深曲线的切线斜率和降深公式的特性得出了确定渗透系数张量的解析公式，结果表明，该公式不仅使计算更简便，而且使得计算值更精确。%To calculate the permeability tensor in fissure medium well flow problems,on the basis of the characteristics of fracture seepage anisotropy aquifer medium,using the theory of fractional differential equation,we establish a time fractional (0.5 order) mathematical model with the level of single fissure medium radial anisotropic unsteady well flow problem.Through the definition and properties of special functions,the fractional derivative and function of Laplace and Fourier transformation get the analytical solution of fractional model of level single fissure medium radial anisotropic nonholonomic well flow.The last use tangent slope of drawdown curve and characteristics of the analytical solution to determine the analytical formula of coefficient of permeability ten-sor.Results show that the formula not only makes the calculation more simple and makes the calculated value more accurate.