多孔介质中粘弹性液体广义流动分析

The generalized flow analysis of non-Newtonian visco-elastic fluid flows in porous media

将分数阶导数引入渗流力学建立了多孔介质中具有松驰特性的非牛顿粘弹性液体的含有分数阶导数的不稳定渗流模型,利用离散逆Laplace变换技巧和广义Mittag Leffler函数研究了多孔介质中非牛顿松弛粘弹性液分数阶流动特征。对任意的分数阶导数得到了精确解,并先求出了长时和短时渐进解,然后用拉普拉斯数值反演Stehfest方法分析无限大地层粘弹性液的流动。结果表明粘弹性流体对分数导数的阶数具有极强的敏感性。

The fractional derivative approach in the seepage mechanics is introduced. A generalized relaxation model of non-Newtonian visco-elastic fluid with the fractional derivatives is built. Exact and asymptotic solutions for some unsteady flows in an infinite and finite reservoir are obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function . The pressure transient behavior of non-Newtonian visco-elastic fluid are studied by using the numerical Laplace transform inversion and asymptotic solutions. The dynamical characteristics of visco-elastic fluid are very sensitive to the order of the fractional derivatives.