Adaptive Nonuniform Grid Dagan's Upscaling Method of Fluid Equation in Porous Media
Kong Fanqun,Liu Fuping,Zhang yu,Yang Changchun
(Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 10010 1,China)

Abstract: In the coarsen grid blocks, firstly, the probability density function of permeability by statistical method is computed, then using Dagan's integration equation the effective permeability by the probability density function of permeability is computed, the pressure distribution has been calculated by the effective permeability in all coarsen grid blocks. In the paper, the adaptive grid technology has been applied to upscaling method of 3D fluid equations in porous media. The fine grid blocks have been automatically adopted and the 3D fluid equations in porous media have also been solved by direct method where permeability or porosity change is abnormity. In the other region the nonuniform upscaling method has been adopted, i.e. using fine grid blocks in the high flow regions of the model. Using the method we have calculated the pressure distribution of the 3D fluid equations in porous media. The results show that the solutions of adaptive nonuniform upscaling method of 3D fluid equations in porous media are very approaching that of adopting fine grid blocks in the regions where the permeability or porosity change is abnormity and very approaching that of adopting coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method.
Keywords: coarse grid blocks, fine grid blocks, flow equation in porous media, effective permeability, porosity, adaptive grid upscaling method.