THE FLOW ANALYSIS OF FLUIDS IN FRACTAL RESERVOIR WITH THE FRACTIONAL DERIVATIVE

作     者：TIAN Ji TONG Deng-ke TIAN Ji Institute of Mechanics, Chinese Academy of Science,Beijing 100080,China Gudong Petroleum Factory of Shengli Petroleum Administration, Dongying 256504,China TONG Deng-ke Department of Applied Mathematics, China University of Petroleum,Dongying 257061, China

作者机构：Institute of Mechanics Chinese Academy of ScienceBeijing 100080China Gudong Petroleum Factory of Shengli Petroleum Administration Dongying 256504China Departmentof Applied Mathematics China University of Petroleum Dongying 257061 China 

出 版 物：《Journal of Hydrodynamics》 (水动力学研究与进展B辑（英文版）)

年 卷 期：2006年第18卷第3期

页      面：287-293页

核心收录：

学科分类：080103[工学-流体力学] 08[工学] 080104[工学-工程力学] 081502[工学-水力学及河流动力学] 0815[工学-水利工程] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the China National 973 Program (Grant No: 2002CB211708) and the Natural Science Foundation of Shandong Province (Grant No: Y2003F01) 

主　　题：fractional calculus porous media fractal,integral transform exact solution 

摘      要：In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional derivative. The flow characteristics of fluids through a fractal reservoir with the fractional order derivative are studied by using the finite integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of fluids flow through an infinite fractal reservoir is studied by using the Stehfest＇s inversion method of the numerical Laplace transform. It shows that the order of the fractional derivative affect the whole pressure behavior, particularly, the effect of pressure behavior of the early-time stage is larger The new type flow model of fluid in fractal reservoir with fractional derivative is provided a new mathematical model for studying the seepage mechanics of fluid in fractal porous media.