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考虑表皮效应竖向非均匀分布,建立各向异性承压层3D稳态井流数学模型,为求得问题的解,首先将表皮效应系数视为分段连续函数,再根据该分段函数将承压层划分成N层,然后通过差分法将问题转化为求解矩阵微分方程边界值问题,最后通过矩阵理论求得相应问题的解。应用数学软件对所求得解进行编程,并应用于实例计算和分析中。结果表明,在距竖井较近处,承压层水头降和流量沿竖向分布均与表皮效应系数函数变化趋势相反,即承压层某深度处的表皮效应系数越大(小),则相应位置的水头降和流量越小(大);而距竖井较远处,仅当竖向渗透系数相对于水平渗透系数较小时,才仍具有前述变化规律;承压层不同深度处的水头降沿径向的分布曲线的幅度值,不仅取决于该处的表皮效应系数大小,而且取决于竖向渗透系数与水平渗透系数相对值大小。
Considering the vertical non-uniform distribution of skin effect, a 3D steady-state well flow mathematical model of anisotropic pressure bearing layer is established. To solve the problem, the skin effect coefficient is considered as a piecewise continuous function. Based on the piecewise function The bearing layer is divided into N layers, and then the problem is transformed into the problem of solving the boundary value problem of matrix differential equation by the difference method. Finally, the solution of the corresponding problem is obtained by matrix theory. Application of mathematical software to solve the programming, and applied to the calculation and analysis of examples. The results show that in the vicinity of the shaft, the water head-down and the flow vertical distribution in the confined layer are opposite to the changing trend of the coefficient of the skin effect coefficient, that is, the larger (smaller) the skin effect coefficient at a depth of the bearing layer, The water head drop and the flow rate are smaller (large) at the location; while the farther away from the shaft, the above variation rules still exist only when the vertical permeability coefficient is smaller than the horizontal permeability coefficient; The amplitude of the radial distribution curve depends not only on the size of the skin effect coefficient, but also on the relative value of the vertical permeability coefficient and the horizontal permeability coefficient.