Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics

Ren-Shi Nie; Yong Ding
February 2010
Natural Science;Feb2010, Vol. 2 Issue 2, p98
Academic Journal
For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spherical flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the effect of wellbore storage. By variable substitution, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the numerical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear percolation type curves in shape and characteristics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical offset of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the influence of the quadratic pressure gradient is very distinct, especially for the low permeability and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in reservoir, therefore the research on nonlinear percolation theory should be strengthened and reinforced.


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