Abstract

The effect of bottom-hole pressure and formation pressure due to a partially penetrating well (PPW) is different from that for an open hole well. In order to analyze the effect of imperfection on pressure response type curves, this paper presents a 3D symmetry porous flow model for circularly partially penetrating wells. Laplace transform and Fourier transform and Bessel functions are applied to obtain the analytical solution of the model. The pressure response and pressure distribution are obtained and the influence on flow regime surrounding the well and pressure response caused by partial penetration are analyzed. Research results show that when the imperfect area tends to zero, the solution of the model can be reduced to the traditional model of the perfect wells presented by Theis, demonstrating the correctness of the solution. The early-time pressure is significantly lower than the case of complete well. The pressure difference between a partially penetrating well and a completely penetrating well decreases with time increasing. Without considering the variation of spatial distribution of flow field due to imperfect well it may bring about errors of formation parameters calculated by perfect well model. Those conclusions improve the seepage model and provide theoretical guidance for the transient pressure data interpretation, formation parameters calculation and productivity prediction of partially penetrating wells. The presented research content furthers the theory of well test analysis, and builds theoretical foundation for the technologies of well testing interpretation and reservoir numerical simulation.

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