A study on nonlinear flow law with deformed media in low permeability reservoir

Abstract

With the continuous improvement of oil exploration and utilization, low permeability reserves have accounted for an increasingly large proportion. However, in low permeability reservoirs, the original permeability and porosity are very low and the relative range of variation of permeability and porosity will dramatically affects the performance of petroleum production, resulting in unsatisfied EOR. Therefore, the flow in the formation is no longer in line with Darcy's law, and the flow equation is strongly nonlinear. As a result, it is necessary to consider the influence of deformed media and the quadratic gradient term in nonlinear partial differential equation of low permeability reservoir model should not be neglected. Based on the percolation characteristics of low permeability layers, this work deduces the flow equation and establishes corresponding mathematical model considering quadratic gradient term. Then the numerical model is built and solved by numerical method. The results show that, in order to avoid certain errors in production process, we should consider the influence of quadratic gradient term. Studying this model with deformed media can guide analysis and application of well test in low permeability reservoirs more scientifically, which has significant theoretical value and practical value.