Improved modeling for fluid flow through porous media

Zaman, Tareq Uz (2018) Improved modeling for fluid flow through porous media. Masters thesis, Memorial University of Newfoundland.

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Abstract

Petroleum production is one of the most important technological challenges in the current world. Modeling and simulation of porous media flow is crucial to overcome this challenge. Recent years have seen interest in investigation of the effects of history of rock, fluid, and flow properties on flow through porous media. This study concentrates on the development of numerical models using a ‘memory’ based diffusivity equation to investigate the effects of history on porous media flow. In addition, this study focusses on developing a generalized model for fluid flow in packed beds and porous media. The first part of the thesis solves a memory-based fractional diffusion equation numerically using the Caputo, Riemann-Liouville (RL), and Grünwald-Letnikov (GL) definitions for fractional-order derivatives on uniform meshes in both space and time. To validate the numerical models, the equation is solved analytically using the Caputo, and Riemann-Liouville definitions, for Dirichlet boundary conditions and a given initial condition. Numerical and analytical solutions are compared, and it is found that the discretization method used in the numerical model is consistent, but less than first order accurate in time. The effect of the fractional order on the resulting error is significant. Numerical solutions found using the Caputo, Riemann-Liouville, and Grünwald-Letnikov definitions are compared in the second part. It is found that the largest pressure values are found from Caputo definition and the lowest from Riemann-Liouville definition. It is also found that differences among the solutions increase with increasing fractional order,

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