Adaptive grid technology is applied to upscaling method of 3D fluid equations in porous media. Where the permeability or porosity change is abnormal, the fine grid blocks are automatically adopted and the 3D fluid equations in porous media is solved by the direct method. In the other regions, the nonuniform upscaling method is adopted, i.e., using fine grid blocks in the high flow regions of the model. Using this method, the pressure distribution of the 3D transient heterogeneous fluid in porous media is calculated. Results show that the solutions by using nonuniform adaptive upscaling method of 3D transient heterogeneous fluid in porous media very approach the solutions by using fine grid blocks in the regions the permeability or porosity is abnormal and very approach the solutions by using coarse grid blocks in the other regions; however, the computation speed by using adaptive upscaling method is 100 times more than that by using fine grid block method.

The sensitivity coefficients to the porosity are derived from the initial boundary value problems for the fluid equations in porous media by the Green's Reciprocity Principle. The sensitivity coefficients of wellbore pressure to the porosity are obtained by the Peaceman's equation and calculated with a numerical method for the 3D transient anisotropic fluid equation in porous media and verified with the direct method. The computed results are in agreement with those obtained with the direct method.