Analyzing fluid flow characteristics in a dual-porosity reservoir with an elastic outer boundary

When we develop petroleum and natural gas reservoirs, we can see a lot of dual-porosity reservoirs with both pores and fractures. Many researchers have studied characteristics of fluid flow in dual-porosity reservoirs with the ideal outer boundary (infinite boundary, closed boundary or constant pressure boundary) but nobody has considered dual-porosity model with the elastic outer boundary (EOB) reflecting the real condition. So there could be large errors in analyzing well-test data for dual-porosity model. In this paper, we establish a percolation model for dual-porosity reservoirs with the EOB and consider the skin factor and wellbore storage. And we obtain its solution in Laplace space by introducing the effective well radius and applying the Laplace transformation. An approximation in Laplace space is also derived by using an asymptotic formula of I0(x) and I1(x). By using Stehfest numerical inversion of Laplace transformation, the solution in the real space is obtained. We compare this model to homogeneous model with the EOB and conventional dual-porosity model, respectively. Comparison results show that the conventional outer boundary conditions are three special cases of the EOB and homogeneous model with the EOB is a special case of dual-porosity model with the EOB. Flow characteristics are analyzed and it is shown that the EOB affects analysis of well-test data through simulation. This study may improve the accuracy of well-test analysis for dual-porosity reservoir.