应力敏感油藏中考虑启动压力和二次梯度的非线性渗流模型

A Nonlinear Flow Model of Stress-sensitive Reservoir For The Start-up Pressure Gradient And The Quadratic Pressure Gradient

从质量守恒原理出发,详细推导出了应力敏感油藏中考虑启动压力梯度和二次压力梯度非线性不稳定渗流偏微分方程。并通过变量代换,将渗流方程拟线性化,最后利用Douglas-Jones预估-校正法求得模型的数值解。讨论了不同参数变化时井底压力的变化规律,做出了典型压力曲线图版。曲线在形态和特征上与线性模型曲线明显不同,不再遵循"0.5线"规则和"单位斜率"规则。启动压力梯度因子影响压力降落曲线晚期上翘段的斜率,该因子越大,曲线上翘程度越大,当其很小时,压力导数曲线出现水平直线段。

This paper deduces the partial differential equation of stress--sensitivereservoir for the nonlinear flow with the start--up pressure gradient and the quad--ratic pressure gradient in detail based on the mass conservation principle. And then quasilinearizating the flow equation with variable substitution,The numerical solution of the flow model was obtained by Dou- glas-Jones predictor corrector method at a constant rate production. The changing rules of pressure when various para-me- ters change. The plots of typical pressure curves were given. The form and characteristics of the curve are different from ones of linear model curve, no longer following＊0. 5 line＊ rules and ＊unit slope＂ rules. Start--up pressure gradient factor affects the slope of pressure drawdown curve in the later, the greater is the value of this factor, the greater is the degree of the curve, when it is very little, the pressure derivative curve appear straight and level section.