科研之友
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摘要
An injection-falloff-production test (IFPT) was originally proposed in Chen et al. (in: SPE conference paper, 2006. doi:10.2118/103271-MS, SPE Reserv Eval Eng 11(1):95-107, 2008) as a well test for the in situ estimation of two-phase relative permeability curves to be used for simulating multiphase flows in porous media. Hence, we develop an approximate semi-analytical solution for the two-phase saturation distribution in an oil-water system during the flowback period of an IFPT according to the mathematical theory of waves. In fact, we show that the weak solution we construct for the saturation equation for the flowback period satisfies the Oleinik entropy condition and hence is unique. In addition, we allow the governing relative permeabilities during the flowback period to be different from the relative permeabilities during injection. Using the saturation solution with the steady-state pressure theory of Thompson and Reynolds, we obtain a solution for the wellbore pressure during the flowback period. By comparing results from our solution with those from a commercial numerical simulator, we show that our approximate semi-analytical solution yields accurate saturation profiles and bottom hole pressures history. The use of very small time steps and a highly refined radial grid is necessary to generate a good solution from a reservoir simulator. The approximate analytical pressure solution developed is used as a forward model to match pressure and water flow rate data from an IFPT in order to estimate reservoir rock absolute permeability and skin factor in conjunction with in situ imbibition and drainage water-oil relative permeabilities.
- 出版日期2018-1
