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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。
Based on the principle of conservation of mass, the partial differential equations of nonlinear instability seepage with stress gradient and secondary pressure gradient in stress-sensitive reservoirs are deduced in detail. Through the variable substitution, the seepage equation is quasi-linearized. Finally, the numerical solution of the model is obtained by Douglas-Jones estimation-correction method. The variation law of bottom hole pressure with different parameters was discussed, and a typical pressure curve chart was made. The curve is significantly different in shape and characteristics from the linear model curve and no longer follows the “0.5 line” rule and the “unit slope” rule. The start-up pressure gradient factor affects the slope of the late upturn segment of the pressure drop curve. The larger this factor is, the greater the upturned curve is. When it is small, the horizontal linear segment of the pressure derivative curve appears.