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Spatial fractional Darcy’s law to quantify fluid flow in natural reservoirs

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  • Chang, Ailian
  • Sun, HongGuang
  • Zhang, Yong
  • Zheng, Chunmiao
  • Min, Fanlu

Abstract

Various formulas describing non-Darcy flow have been applied to quantify fluid flow in natural geological media, while there is no universal law or formula that can reliably describe the complex relationship between the flow rate and the pressure gradient for single-phase fluid flow in natural oil/gas reservoirs. This study aims at proposing and evaluating a spatial fractional Darcy’s law model for the calculation of the flow rate of fluids in natural heterogeneous oil/gas reservoirs at any scale. Experiments documented in literature are revisited to identify the transport characteristics of fluid flow in natural media with complex heterogeneity and structures, including for example discontinuous and/or interconnected pores. The fitting exercises show that the spatial fractional Darcy’s law can felicitously depict the flow properties and match well the experimental data shown in seepage curves. The model parameters can also be reasonably simplified, given the possible physical interpretation closely related to the medium structure.

Suggested Citation

  • Chang, Ailian & Sun, HongGuang & Zhang, Yong & Zheng, Chunmiao & Min, Fanlu, 2019. "Spatial fractional Darcy’s law to quantify fluid flow in natural reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 119-126.
    • Handle: RePEc:eee:phsmap:v:519:y:2019:i:c:p:119-126
    DOI: 10.1016/j.physa.2018.11.040
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    References listed on IDEAS

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    1. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
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    Cited by:

    1. Hanif, Hanifa, 2022. "A computational approach for boundary layer flow and heat transfer of fractional Maxwell fluid," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 1-13.
    2. Fernando Alcántara-López & Carlos Fuentes & Rodolfo G. Camacho-Velázquez & Fernando Brambila-Paz & Carlos Chávez, 2022. "Spatial Fractional Darcy’s Law on the Diffusion Equation with a Fractional Time Derivative in Single-Porosity Naturally Fractured Reservoirs," Energies, MDPI, vol. 15(13), pages 1-11, July.
    3. Zhou, Ziyi & Zhang, Haixiang & Yang, Xuehua, 2024. "CN ADI fast algorithm on non-uniform meshes for the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamics," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    4. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    5. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

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