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The Similar Structure of Solutions In Fractal Multilayer Reservoir Including A Quadratic Gradient Term

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Abstract

When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries (infinite boundaries, constant pressure boundaries and closed boundaries). Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.

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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China

    Wei Li & Xiao-ping Li

  2. Institute of Applied Mathematics, Xihua University, Chengdu, 610039, China

    Shun-chu Li & Quan-yong Li

Authors
  1. Wei Li
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  2. Xiao-ping Li
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  3. Shun-chu Li
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  4. Quan-yong Li
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Corresponding author

Correspondence to Wei Li.

Additional information

Project supported by the National Science and Technology Major Project of China (Grant No. 2008ZX50443-14), the National Basic Research Program of China (973 Program, Grant No. 2011CB201005).

Biography: LI Wei (1983-), Male, Ph. D.

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Li, W., Li, Xp., Li, Sc. et al. The Similar Structure of Solutions In Fractal Multilayer Reservoir Including A Quadratic Gradient Term. J Hydrodyn 24, 332–338 (2012). https://doi.org/10.1016/S1001-6058(11)60252-7

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  • DOI: https://doi.org/10.1016/S1001-6058(11)60252-7

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