考虑非线性二次梯度项的不稳定渗流解析解及其应用  

The Analytical Solution to the Problem of Nonlinear Unsteady Seepage Equation with Quadratic Gradient Term

作　　者：杨宇[1] 刘世界[1] 刘鑫 彭小东 

机构地区：[1]成都理工大学能源学院,成都610059 [2]中海石油(中国)有限公司湛江分公司,湛江524057

出　　处：《科学技术与工程》2012年第31期8190-8193,共4页Science Technology and Engineering

基　　金：国家十二五重大专项(2011ZX05014-004-004HX)资助

摘　　要：在常规的地下流体渗模型求解过程中,为了简化计算,一般忽略渗流连续方程的二次梯度项。但是,在一些对求解精度要求高的渗流问题中,如果忽略渗流连续方程的二次梯度项,将产生显著的误差。使用了Boltzman变换和常数变易法,导出了无限大地层的解析解。对考虑二次梯度项与忽略该项的解进行差异分析。结果表明:随着时间、产量的增大,渗透率的降低,差异有变大的趋势。而随半径的减小,差异也有变大的趋势。最后,对解析解进行简化,导出了可以用于试井分析的简化公式。In the conventional seepage model of underground fluid, the quadratic gradient term of the seepage continuity equation is ignored to simplify the computation, h has been proved that this kind of simplification will re- sult in significant errors under some specific conditions. Herein the Boltzmann transformation and constant variation are adopted to derive the analytical solution of the infinite formation. The difference between the solution which consider the quadratic gradient term and the conventional one is analyzed, and the results show that, with the in- crease of time and production, the lower the permeability, the larger variance will become, whereas with the de- crease of radius, the variance become larger. Finally, the analytical solution is simplified for well testing.

关 键 词：二次梯度项 Boltzmann变换 常数变异法 解析解 试井 

分 类 号：TE312[石油与天然气工程—油气田开发工程]