非牛顿流体两相渗流问题的摄动解

本文用奇异摄动法结合正则摄动法求解了考虑毛管力因素时多孔介质中弱非牛顿流体的两相驱替问题,得到了分流函数和湿相饱和度的渐近解析解。所得结果同数值解和经典的牛顿流体两相渗流结果进行了比较,并着重讨论了非牛顿因素的影响。

A PERTURBATION SOLUTION FOR NONNEWTONIAN FLUID TWO-PHASE FLOW THROUGH POROUS MEDIA

This paper deals with the problem of nonnewtonian fluid two-phase displacement. The wetting fluid is assumed to be nonnewtonian one and the flow of it in porous media obey the power law equation, while the nonwetting fluid is assumed to be newtonian one and the flow of it follow the linear Darcy's law. Porous media and the fluids in it are all incompressible. In the paper, the regular perturbation method is first used to find the fractional flow function for the wetting fluid with the nonnewtonian exponent being taken as perturbation parameter. Second, the feature of motional boundary layer in saturation propagation is elucidated by analysing and comparing the effects of nonlinear convection and capillary dispersion according to the mathematical model of the problem. Then, choosing the capillary pressure group as small parameter, the Boundary Layer Method of singular perturbation is used to solve a nonlinear convection-dispersion equation. The saturation distributions in and out the capillary dispersion zone are obtained, and the discontinuity relation at the front of displacement in given by the matching condition. Finally a uniformly valid asymptotic analytical solution held in all flow region for the saturation is composed by the additive composition. Accuracy of the solution and validity of the method used are verified by comparing the results obtained with that of classical one for the newtonian case and that obtained by numerical technique. The influences oi nonnewtonian exponent and capillary pressure are discussed.