The elasticity of the outer boundary and the solution of two-region composite reservoir seepage model

Abstract

Considering the characteristic of the outer boundary of the two-region composite reservoir has elasticity, firstly, a new two-region composite reservoir seepage model which considers the wellbore storage and effective well radius is established to describe the seepage laws of the two-region composite reservoir more accurately. Then, by combining the Laplace transform and the similar construction method, the solution of dimensionless bottom hole pressure is obtained in the Laplace space. Meanwhile, the solution is also inverted into real space by means of the Stehfest numerical inversion method. Finally, the characteristic curves of dimensionless bottom hole pressure and its derivative are drawn, and the influence of elastic coefficient and reservoir parameters on the characteristic curves is also analyzed. The results reveal that the characteristic curves have affine similarities, and the characteristic curves under the elastic outer boundary condition are always between the closed outer boundary condition and constant pressure outer boundary condition. It can be seen that the conventional three idealized outer boundary conditions (closed, constant pressure and infinite) of two-region composite reservoirs are actually three special cases of elastic outer boundary condition. The introduction of elastic outer boundary condition not only expands the range of data interpretation reasonably, but also shows the actual state of the outer boundary of the two-region composite reservoir better. The similar construction method can avoid complicated and trivial operation processes, and greatly accelerate the model solving speed. The findings of this study can help for better understanding of the real situation of the outer boundary of the two-region composite reservoir, which improves the matching degree between the theoretical model and the actual reservoir, and provides convenience for the development of related well test analysis software.