考虑启动压力梯度的致密气藏渗流数学模型解析解研究

对存在启动压力梯度的致密气藏不稳定渗流数学模型进行分析时,常用的方法是在拉式空间运用格林函数法进行求解,但这个解无法反演到实空间而获得解析解.根据拉式变换及其逆变换的性质引入了附加函数,得到了形式简明的实空间上的解析解.通过对比多组解析解和数值反演的结果表明该解析解的计算精度在5%以内,因而此解析解可以在工程中应用.

Study on the Analytical Solution of Mathematical Model for the Tight Gas Reservoir about Start-up Gradient

When analyzing the mathematical model of the unsteady flow in the tight gas reservoir which has start up pressure gradient,its usual method is using Green Function to obtain the solution in the Laplace Space,yet which cannot be inverted to real space to acquire the analytical solution.Based on the nature of Laplace transformation and inverse Laplace transformation,this paper introduces the additional function and obtains the concise analytical solution in the real space.The comparison of the results of analytic solution and numerical inversion shows that,the calculation accuracy is within 5 percent,and thus it can be applied to the engineering.