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在天然气藏中，底水气藏占有很重要的地位，因而水锥的控制及数值模拟就成为气藏开发的一个重要问题，文章提供了计算气井水锥自由边界问题的边界元方法。首先把水锥剖面视为由气、水两区域构成，指出了以气体拟压力作为未知量的变系数椭圆型方程的自由边界问题；其次使用特殊的基本解和直接边界积分给出了问题的混合边界积分方程组，再利用周期变换和机械求积法导出了离散方程组。周期变换提高了求解的精度，而机械求积法简化了离散方程组系数矩阵的生成。由于离散方程组是建立在边界上，故网格点少，只包含边界处的未知量，因而只需要较小的计算量就可求解，利用迭代算法能很快就能确定水锥的位置。实算表明，本方法简单易行、计算量小，能够提高模拟质量，有利于制定气井开采方案。

BOUNDARY ELEMENT METHOD OF FREE BOUNDARY ISSUES OF STATIONARY WATER CONE FOR GAS WELL 1)

Gas reservoirs with bottom water account for big percentage in all gas reservoirs, so the control and numerical simulation of the water cone is very important for gas reservoir production. The article presents the boundary element method to compute the free boundary of the water cone for gas wells. At first, it is assumed the section of the water cone consists of both gas/water zones. Taking the gas pseudo-pressure as the unknown quantity, the free boundary problem is proposed for the elliptic equation with variable coefficient. Then, using the special basic solution and the direct boundary integral, the integral equation group is derived for the mixed boundary of the problem. And with periodical transformations and mechanical quadrature methods, the divergent equation group is obtained. The periodical transformations improve the solution accuracy. The mechanical quadrature methods simplify the creation of the coefficient matrix of the divergent equation group. Since the divergent equation group is established at the boundary, its net points are few, only including the unknown quantity at the boundary, and a little computation is needed to make the solution. The position pf the water cone can be found quickly by the iterative method. The real case computation shows the method is easy to practice, few to compute, able to improve the simulation quality, and favor to make the exploitation program for gas wells.