A modified memory-based mathematical model describing fluid flow in porous media
暂无分享,去创建一个
Kassem Mustapha | M. Enamul Hossain | Abiola D. Obembe | Sidqi A. Abu-Khamsin | M. Hossain | S. Abu-Khamsin | K. Mustapha
[1] Santos B. Yuste,et al. An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations , 2004, SIAM J. Numer. Anal..
[2] M. Hossain,et al. A Comprehensive Material Balance Equation with the Inclusion of Memory During Rock-Fluid Deformation , 2009 .
[3] C. Lubich. Discretized fractional calculus , 1986 .
[4] Francisco J. Sánchez-Sesma,et al. Theory and simulation of time-fractional fluid diffusion in porous media , 2013 .
[5] Xiaoyun Jiang,et al. Parameter estimation for the fractional fractal diffusion model based on its numerical solution , 2016, Comput. Math. Appl..
[6] Reyadh A. Almehaideb. Improved Correlations for Fluid Properties of UAE Crude Oils , 2003 .
[7] Shyam L. Kalla,et al. Numerical treatment of fractional heat equations , 2008 .
[8] B. Henry,et al. The accuracy and stability of an implicit solution method for the fractional diffusion equation , 2005 .
[9] Diego A. Murio,et al. Implicit finite difference approximation for time fractional diffusion equations , 2008, Comput. Math. Appl..
[10] Guanrong Chen,et al. Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching , 2013, Comput. Math. Appl..
[11] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[12] D. W. Peaceman. Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability , 1983 .
[13] J. Auriault,et al. Homogenization of Coupled Phenomena in Heterogenous Media , 2009 .
[14] Raphael Blumenfeld,et al. Failure of isotropic continuous-time random walks to model finite-size particle diffusion in porous media and an effective modification , 2015 .
[15] Koo-Chul Lee,et al. Nonlinear correction to Darcy's law for a flow through periodic arrays of elliptic cylinders , 2001 .
[16] Mark M. Meerschaert,et al. A second-order accurate numerical approximation for the fractional diffusion equation , 2006, J. Comput. Phys..
[17] Vladimir Mityushev,et al. Nonlinear correction to Darcy’s law for channels with wavy walls , 2013 .
[18] José António Tenreiro Machado,et al. Fractional model for malaria transmission under control strategies , 2013, Comput. Math. Appl..
[19] J. H. Abou-Kassem,et al. Petroleum reservoir simulation : a basic approach , 2006 .
[20] M. Caputo,et al. Experimental and theoretical memory diffusion of water in sand , 2003 .
[21] Rina Schumer,et al. Incorporating Super-Diffusion due to Sub-Grid Heterogeneity to Capture Non-Fickian Transport. , 2015, Ground water.
[22] M. Caputo. Models of flux in porous media with memory , 2000 .
[23] Santos B. Yuste,et al. On an explicit finite difference method for fractional diffusion equations , 2003, ArXiv.
[24] Rodolfo Camacho Velazquez,et al. Interference Tests Analysis in Fractured Formations With a Time-Fractional Equation , 2012 .
[25] R. Raghavan,et al. Fractional diffusion in rocks produced by horizontal wells with multiple, transverse hydraulic fractures of finite conductivity , 2013 .
[26] Rajagopal Raghavan,et al. Rate Decline, Power Laws, and Subdiffusion in Fractured Rocks , 2017 .
[27] S. Havlin,et al. Diffusion and Reactions in Fractals and Disordered Systems , 2000 .
[28] Santos B. Yuste,et al. Weighted average finite difference methods for fractional diffusion equations , 2004, J. Comput. Phys..
[29] Christopher L. MacDonald,et al. Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory , 2015, J. Comput. Phys..
[30] M. Caputo,et al. Diffusion in porous layers with memory , 2004 .
[31] H. R. Hicks,et al. Numerical methods for the solution of partial difierential equations of fractional order , 2003 .
[32] O. Ozcan,et al. Fractional diffusion in naturally fractured unconventional reservoirs , 2014 .
[33] Fawang Liu,et al. Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term , 2009, J. Comput. Appl. Math..
[34] Monica Moroni,et al. Flux in Porous Media with Memory: Models and Experiments , 2010 .
[35] Michele Caputo,et al. Diffusion with space memory modelled with distributed order space fractional differential equations , 2003 .
[36] Yufeng Xu,et al. Numerical and analytical solutions of new generalized fractional diffusion equation , 2013, Comput. Math. Appl..
[37] G. Zaslavsky. Chaos, fractional kinetics, and anomalous transport , 2002 .
[38] I. Podlubny. Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .
[39] Abdul-Aziz Al-Helali,et al. A MATHEMATICAL MODEL FOR THERMAL FLOODING WITH EQUAL ROCK AND FLUID TEMPERATURES , 2015 .
[40] Yu-xin Zhang,et al. Notes on Implicit finite difference approximation for time fractional diffusion equations [Comput. Math. Appl. 56 (2008) 1138-1145] , 2011, Comput. Math. Appl..
[41] Michele Caputo,et al. Diffusion of fluids in porous media with memory , 1999 .