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将分数阶导数和分形维数及谱维数引入渗流力学建立了分形油藏具有松弛特性的非Newton黏弹性液体的含有分数阶导数的不稳定渗流模型,引入一种新的积分变换,并利用此积分变换和离散逆Laplace变换技巧及广义Mittag-Leffler函数研究了分形油藏中非Newton松弛黏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,并求出了无限大地层的长时和短时渐近解,用Laplace变换求逆数值反演Stehfest方法分析无限大地层黏弹性液的流动.结果表明黏弹性特征越明显的流体对分数导数的阶数越具有敏感性.新的积分变换为研究分形介质渗流问题的力学性质提供了新的解析工具.
By introducing fractional derivative and fractal dimension and spectral dimension into seepage mechanics, an unsteady seepage model with fractional derivative of non-Newtonian viscoelastic liquid with fractal reservoir is established. A new integral transform is introduced and used The integral transform and discrete inverse Laplace transform techniques and the generalized Mittag-Leffler function are used to study the fractional flow characteristics of non-Newtonian viscoelastic fluids in fractal reservoirs. Exact solutions of arbitrary fractional derivatives are obtained and the infinite stratum Term and short-time asymptotic solutions, the Stehfest method is used to analyze the viscoelastic fluid flow in infinite stratum with the Laplace transform inverse numerical inversion method. The results show that the more viscous-elastic fluid is, the more sensitive the order of fractional derivative is. The new integral transformation provides a new analytical tool for studying the mechanical properties of fractal fluid percolation problems.