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本文根据“影响半径”的概念,找到了双重介质弹性渗流方程组的近似解。实质上该近似解满足平均的双重介质质量守恒方程,即将其代入弹性渗流方程引起的残差加权平均等于零。近似解揭示了井底压力变化大致可分三个阶段:初期的半对数直线段,中期的平缓曲线段以及后期的平行半对数直线段。在时间不是很短的条件下,近似解与精确解符合得较好。由于公式结构简单可以在矿场上推广应用。应用本文的求解方法亦可得到非均质裂缝—孔隙介质弹性渗流方程组的近似解。
In this paper, according to the concept of “radius of influence”, we find the approximate solution of the equations of elasticity for two-medium elastic seepage. In essence, the approximate solution satisfies the averaged two-medium mass conservation equation, that is, the weighted average of the residuals caused by its substitution into the elastic seepage equation is equal to zero. The approximate solution reveals that the bottom hole pressure change can be roughly divided into three stages: the initial semi-logarithmic straight line, the medium flat curve and the late parallel semi-logarithmic straight line. In the condition that the time is not very short, the approximate solution and the exact solution are in good agreement. Due to the simple formula structure can be promoted in the mine. The approximate solutions to the elastic seepage equations in inhomogeneous fracture-pore media can also be obtained by applying this method.