水平井无限井排产能公式──Muskat公式的推广

PRODUCTIVITY FORMULA OF AN INFINITE HORIZONTAL WELL ARRAY-AN EXPANSION OF MUSKAT FORMULA

应用镜像法将二维单井排水平井问题等效为带状区域中单口水平井问题，利用多次保角变换将此二维带状区域穿透比小于1的单口水平井映射为穿透比等于1的带状地层，从而求解出二维地层中水平井单井排的稳态压力分布函数的解析表达式。只需让水平井水平段长度趋于0，即可以证明它是Muskat公式的推广。利用拟三维思想和等值渗流阻力法求出上、下边界封闭的单井排水平井产能公式。

The paper studies the steady state now for a 2D model of a horizontal well array. It applies the imaging method to equal theproblem of a 2D horizontal well array to that of a single horizontal well in band-region and uses conformal transmission tochange 2D band-region of a single horizontal well with punch-ratio lower than one into that with punch-ratio equal to one.Thus the analytical formula for calculating pressure distribution of this horizontal well array are derived. It is proved that thisis an expansion of Muskat formula for a vertical well array only if the length of the horizontal section of a horizontal well isnear to zero (L→0). To obtain the productivity of a horizontal well array in the formation with impermeable overburden andunderburden, the method of a preudo 3D model and equivalent flow resistance is considered.