考虑二次梯度项影响的非线性不稳定渗流问题的精确解

考虑了二次梯度项影响的非线性径向流动问题的无限大地层和有界地层渗流模型．在井底定流量和定压生产时，对无限大地层及有界地层(包括封闭和定压地层)六种情况，利用广义Weber变换和广义Hankel变换求得了实空间的解析解，分析了非线性压力解与线性压力解的差异，发现在晚时段其差异可达8%以上．因此在试井长时要考虑二次梯度项的影响．

Exact Solutions for Nonlinear Transient Flow Model Including a Quadratic Gradient Term

The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered.The difference between the nonlinear pressure solution and linear pressure solution is analyzed.The difference may be reached about 8 % in the long time. The effect of the quadratic gradient term in the large time well test is considered .