Study On Non-darcy Flow Behavior And Inverse Problem In Low-permeability Heterogenous Reservoirs

There is considerable evidence that the fluid flow in low-permeability reservoirs is non-Darcy flow at low velocity. Many problems haven抰 been resolved although some scholars have investogated the non-Darcy flow. In this work, we have carried out a comprehensive study on the Non-Darcy single-phase flow behavior in heterogeneous low-permeability reservoirs and the identification of reservoir parameters based on inverse problem theory. First, we have generate a general math model involving a threshold pressure gradient under the condition of multi-dimension, multi-phase, and heterogeneous reservoirs, and discussed the relationship between the threshold pressure gradient and reservoir parameters. Secondly, We have developed a finite difference simulator of the fluid flow through heterogeneous reservoirs, and implemented a lot of numerical computations in consideration of some situations such as homogeneous media, anisotropic media, and fractures formation. It is showed by our computation that the reservoir pressure falls rapidly when the threshold pressure gradient has been incorporated in the simulator. We have analyzed type curves of pressure transient data in radially heterogeneous reservoirs where the Non-Darcy flow at low velocity appears in the light of flowrate-average theory of Non-Darcy flow. We have given some equations of the pressure and its derivative influenced by the threshold pressure gradient. Motivated by the ideas of free boundary theory, we have obtained a more accurate integral solution than Wu Yushu?s, and interpreted practical examples by using an automated well test match technique. We have extended theoretically not only the Carter et al method for computing sensitivity coefficients to single-phase 2 problems, but also the rigorous adjoint method proposed by Wu et aI for computing sensitivity coefficients to two-phase problems to the estimate the sensitivity in low- permeability reservoirs. Our sensitivity coefficient expressions considered the cases of the weLlbore pressure and the wellbore rate, multi-layer reservoirs, and they are simplified into the Darcy flow situation when the threshold pressure gradient is equal to zero. Our numerical solutions indicate that the sensitive coefficients in low- permeability reservoirs are influenced by threshold pressure gradient. Finally, We have presented a technique to determine the parameter distribution conditioning dynamic data in low-permeability reservoirs, and proposed and accomplished procedures for actual applications.