In this paper, a relative permeability prediction method considering the effects of capillary pressure and threshold pressure gradient in a low permeability fractal porous medium is established and analyzed based on the fractal approximation model that porous medium consist of a bundle of tortuous capillaries. With this method, every parameter has clear physical meaning without empirical constants, and the model's predictions have a good agreement with experimental data. In addition to this, it makes some discussions that how the characteristic parameters (such as tortuosity fractal dimension, pore fractal dimension, ratio of minimum-maximum capillaries diameters and threshold pressure gradient) influence the relative permeability. This study may be conducible to a better understanding of the mechanism for transient two-phase flow in the low permeability fractal porous medium.
The production decline type curves are considered as a robust technique to interpret the production data and obtain the flow parameters, the original gas in place, etc. However, most of the previous models have focused on the primary depletion with a closed boundary, rather than on the secondary depletion with a water influx/waterflood. Therefore, in this study, a transient flow model considering the water influx/waterflood is developed. Subsequently, the functions of the production decline type curves for a vertical well with a water influx/waterflood are derived based on the material balance equation. In other words, the theory of Blasingame production decline analysis is extended to the water influx/waterflood reservoir. Further advanced Blasingame production decline type curves for a vertical well in water influx/waterflood reservoirs are generated. Compared with Blasingame type curves without a water influx/waterflood, the behavior of the ones presented in this study is quite different at the boundary. Thereafter, the effects of the relevant parameters, including the dimensionless maximum water influx, the dimensionless beginning time of the water influx, and the dimensionless external boundary radius, are studied on type curves. Finally, Blasingame type curves for a vertical well in water influx/waterflood reservoirs are verified through a field case study. This work provides very meaningful references for reservoir engineers working on the evaluation of the water influx and the estimation of the beginning time of the water influx by matching the developed type curves with the actual field data.
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