| In this research, a new pressure transient test consisting of a traditional injection/falloff followed by a flow period when we produce oil and injected water, an injection/falloff/production test (IFPT), is proposed to estimate relative permeabilities, reservoir permeability and well skin factor for the water-oil two-phase problem. An automatic history match code has been developed to estimate parameters defining relative permeabilities, absolute permeability and well skin factor by matching measured data from the test. Two parameterizations of relative permeability curves are considered, a power law model and a more flexible B-spline representation. In this research, an analytical solution for the pressure response was obtained for the case where capillary pressure was negligible. For the case where capillary pressure is significant, we were forced to combine analytical method with a finite difference solution of the Buckley-Leverett equation to obtain the pressure solution during the flow back period. We show that the new IFPT yields more accurate estimates of relative permeabilities than can be obtained with a conventional injection/falloff test. The analytical solution assumes constant injection rate; but we show that good parameter estimates can still be obtained by the analysis method under reasonable flow rate fluctuations. |
