二次压力梯度三孔渗流模型及非线性渗流特征

A triple-porosity flow model and its nonlinear flow characteristics with considering quadratic pressure gradient

裂缝孔洞型三孔介质储层渗流的非线性特征十分明显,其渗流模型中的非线性项不应被忽略。针对裂缝孔洞型三孔介质储层,建立了二次梯度不稳定渗流数学模型。利用变量代换,将渗流模型线性化,求得了拉氏空间下的解析解,采用数值反演法得到了实空间的解。利用模型的解,编程绘制了典型的非线性渗流特征曲线,其反映了裂缝孔洞型三孔介质储层溶蚀孔洞和基质分别向裂缝窜流的特殊流动阶段。此外,分析了二次压力梯度非线性系数、溶洞向裂缝窜流的窜流系数、基质向裂缝窜流的窜流系数等对渗流特征曲线的影响。最后,通过对比常规线性渗流模型的渗流特征曲线,定量研究了受不同二次压力梯度非线性系数影响时非线性与线性渗流曲线之间的差异。结果表明,因受二次压力梯度非线性系数的控制,非线性渗流特征曲线明显偏离线性渗流特征曲线,且偏离量随时间和非线性系数的增加而增加。新建立的二次压力梯度三孔渗流模型,可精准描述缝洞型碳酸盐岩储层的渗流特征。

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 curvesaffected by the nonlinear quadratic pressure gradient factor was quantitative studied. The results show that affectedby the nonlinear quadratic pressure gradient factor,the nonlinear flow curves obviously deviate from linear flowcurves,and the deviations increase with the elapse of time and the increase of the nonlinear quadratic pressuregradient factor. The established triple-porosity flow model with considering quadratic pressure gradient term canbe used to describe the porous flow characteristics of fractured-vuggy carbonate reservoir more precisely.