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目前在低渗透储层的试井模型中,常采用具有平均启动压力梯度的拟线性渗流方程,然而拟线性渗流方程只能反映低渗透流动的启动压力梯度特征,不能描述流动的非线性特征。三参数非线性渗流方程既反映了启动压力梯度特征,也描述了非线性凹形曲线。为了提高致密气藏试井资料的解释精度,完善低渗透非线性试井理论,建立了一种基于三参数非线性渗流方程的致密气藏数值试井模型。利用有限差分方法求解模型,获得了井底压力响应曲线及储层压力分布。分析了压力响应曲线和压力分布特征,对比了三参数非线性模型与拟线性模型的结果,并研究了最小启动压力梯度和平均启动压力梯度的影响。研究结果表明:系统径向流阶段的压力导数曲线偏离0.5线,压降曲线的上翘幅度取决于平均启动压力梯度,压力恢复曲线的上翘幅度取决于平均启动压力梯度与最小启动压力梯度的差值。外边界响应的早晚和动边界扩展速度取决于最小启动压力梯度。
At present, the quasi-linear seepage equation with average starting pressure gradient is often used in the well testing model of low-permeability reservoirs. However, the quasi-linear seepage equation can only reflect the starting pressure gradient characteristic of low-permeability flow and can not describe the nonlinear characteristics of flow. The three-parameter nonlinear seepage equation not only reflects the characteristics of starting pressure gradient, but also describes the nonlinear concave curve. In order to improve the interpretation accuracy of well test data in tight gas reservoirs and perfect the low permeability nonlinear well test theory, a numerical well test model of tight gas reservoirs based on the three parameter nonlinear seepage equation was established. The finite difference method was used to solve the model, and the bottom hole pressure response curve and reservoir pressure distribution were obtained. The pressure response curves and pressure distributions were analyzed. The results of the three-parameter nonlinear model and the quasi-linear model were compared. The effects of the minimum starting pressure gradient and the average starting pressure gradient were also studied. The results show that the curve of pressure derivative in the radial flow stage of the system deviates from the line 0.5 and the upwelling amplitude of the pressure drop curve depends on the average starting pressure gradient. The upturn amplitude of the pressure recovery curve depends on the average starting pressure gradient and the minimum starting pressure gradient Difference. The response of the outer boundary to the morning and evening and the dynamic boundary expansion rate depends on the minimum starting pressure gradient.