关键词: 二次压力梯度, 渗流模型, 渗流特征, 非线性, 三孔介质

Abstract: The flow of fluids in naturally fractured-vuggy carbonate reservoirs is of strong nonlinear characteristics;therefore,the nonlinear term in a triple-porosity flow model should not to be ignored. For a naturally fracturedvuggy carbonate reservoir,a nonlinear triple-porosity flow model with the consideration of quadratic pressure gradient was established. By using variable substitution,the model can be linearized,and an analytical solution in Laplace space was obtained. A solution with the numerical inversion in real space of the linearized model were obtained. The nonlinear flow characteristics curves were plotted by programming the model solution. The curves reflect the special stage characteristics of inter-porosity flow from vug to fracture systems and matrix to fracture systems respectively. The influences of the fixed model parameters on the type curves were qualitatively and quantitatively studied,including quadratic pressure gradient nonlinear term,the inter-porosity flow factor of fluid from vug to fracture systems,inter-porosity flow factor of fluid from matrix to fracture systems. Finally,by comparing flow characteristic curves of conventional linear flow model,the difference of linear and nonlinear curves affected by the nonlinear quadratic pressure gradient factor was quantitative studied. The results show that affected by the nonlinear quadratic pressure gradient factor,the nonlinear flow curves obviously deviate from linear flow curves,and the deviations increase with the elapse of time and the increase of the nonlinear quadratic pressure gradient factor. The established triple-porosity flow model with considering quadratic pressure gradient term can be used to describe the porous flow characteristics of fractured-vuggy carbonate reservoir more precisely.

Key words: quadratic pressure gradient, porous flow model, porous flow characteristics, nonlinearity, tripleporosity media