基于三参数非线性渗流的致密气藏数值试井分析

Numerical well test analysis of tight gas reservoirs based on the three parameter nonlinear seepage

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。

The well testing models in low permeability reservoir are normally realized by using pseudo-linear flow equation with the average start-up pressure gradient. However, the pseudo-linear flow equation can only reflect the characteristics of start-up pressure gradient in low permeability reservoir. It cannot describe the characteristic of nonlinear flow.The three-parameter nonlinear seepage flow equation not only reflects the characteristics of the starting pressure gradient,also describes the non-linear concave curve.In order to improve the interpretation accuracy of the well test data in tight gas reservoir and perfect the nonlinear well testing theory,this paper presents a nonlinear numerical well testing model based on the three-parameter nonlinear seepage flow equation.With the model, the wellbore pressure response curves and pressure fields were obtained by using finite difference method. The characteristics of pressure response curves and pres- sure fields were analyzed.Effects of minimum start-up pressure gradient and average start-up pressure gradient on pressure response curves and pressure fields were studied.The results proved that the pressure derivative curves in radial flow phase deviating from the 0.5 line. The upward amplitude of pressure drop curves depends on the average start-up pressure gradient; the upward amplitude of pressure buildup curves depends on the difference between the average slart-up pressure gradient and the minimum start-up pres- sure gradient.Response time of the out boundary depends on the minimum starting pressure gradient.