Non-Darcy Flow Analysis Of Fluid In The Low Permeability Reservoir Including The Effects Of The Quadratic-Gradient Term

With the development of petroleum industry in China, the proportion of low permeability oil fields in development is more and more large. In order to develop these oil fields reasonably and efficiently, we should fully recognize the special percolation characteristics of these low permeability reservoirs. According to the assumption of slightly compressible fluid, the quadratic-gradient term in nonlinear partial differential equation of the traditional models for describing percolation regulation is usually neglected. This method is questionable for low permeability reservoirs. It is known that the neglect of the quadratic-gradient term results in errors for large values of well-test time. In addition, the fluid flowing boundary extends outwards continuously with time is the remarkable feature of low permeability reservoirs.Starting with analyzing the percolation characteristics of low permeability oil layer, the physical meaning and percolation regulation that there is the threshold pressure gradient in the process of flow are expounded in this paper. Here, not only the influence of the quadratic-gradient term, moving boundary, skin effect and wellbore storage, but also the characteristics of non-Darcy flow in low-permeability reservoirs are considered for the flow system of the low permeability reservoirs. The flow model of the single-porosity and the flow model of the double-porosity in low permeability reservoirs are built. The numerical methods for the models are researched, and the numerical programs are designed in this paper. Using the programs, satisfactory numerical solutions for the models have been gotten. The changing rules of pressure when various parameters change and the moving rule of the moving boundary are addressed in this paper. The changing rule of the difference between the pressure solution of traditional model and the new model considering the quadratic-gradient term is analyzed. The plots of typical pressure curves are given, and the results can be applied to well-test analysis.