河道油藏的自适应网格积分方程粗化算法

Upscaling method of adaptive grid integral equation for channel reservoir

本文以河道的观测深度为确定性数据由贝叶斯理论通过随机建模的方法生成横截面为抛物线形状的河道油藏边界面。在粗网格内先统计渗透率在粗化网格的概率分布,然后由渗透率积分方程利用渗透率在粗化网格中的概率分布计算粗化网格的等率渗透率,再利用等效渗透率计算粗化网格的压强分布。计算压强时并将渗透率自适应网格技术应用于河道油藏的粗化算法中。在渗透率或孔隙度变化异常区域自动采用精细网格,用直接解法求解渗透率或孔隙度变化异常区域的压强分布,整个区域还采用了不均匀网格。利用本文方法计算了河道油藏的压强分布,结果表明河道油藏的不均匀自适应网格积分方程粗化算法的解在渗透率或孔隙度异常区的压强分布规律更逼近采用精细网格的解,在其他区域压强分布规律非常逼近粗化算法的解,但计算的速度比采用精细网格提高了100多倍。

The bounding surfaces of channel, whose crosssectional shape is parabolic, have been simulated with hard data (observed data) by Bayesian stochastic theory. In the coarse grid blocks, firstly the probability density function of permeability is calculated by statistical method, then the Dagan's integral equation is used to compute the effective permeability from the calculated probability density function of permeability, finally, the pressure is calculated by use of the effective permeability in all coarse grid blocks. In this paper adaptive grid technilogy has been applied to upscaling method of channel reservoir. Where the permeability or porosity change is abnormal, the fine grid blocks are automatically adopted and the 3D fluid equations in porous media are solved by direct method. In other region, the nonuniform upscaling method is adopted, i.e. fine grid blocks is used in the high flow regions of the model. Using this method we have calculated the pressure distribution of the channel reservoir. The results show that the solutions of nonuniform adaptive integral equation upscaling method of channel reservoir approach well the solutions of adopting fine grid blocks in the regions where the permeability or porosity being abnormal and approach the solutions of adopting coarse grid blocks in other region. However, the computational speed of adaptive integral equation upscaling method is 100 times more than that adopting fine grid block method.