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Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure

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  • Razminia, Kambiz
  • Razminia, Abolhassan
  • Torres, Delfim F.M.

Abstract

We obtain an analytical solution for the pressure-transient behavior of a vertically hydraulic fractured well in a heterogeneous reservoir. The heterogeneity of the reservoir is modeled by using the concept of fractal geometry. Such reservoirs are called fractal reservoirs. According to the theory of fractional calculus, a temporal fractional derivative is applied to incorporate the memory properties of the fractal reservoir. The effect of different parameters on the computed wellbore pressure is fully investigated by various synthetic examples.

Suggested Citation

  • Razminia, Kambiz & Razminia, Abolhassan & Torres, Delfim F.M., 2015. "Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 374-380.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:374-380
    DOI: 10.1016/j.amc.2014.12.124
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    References listed on IDEAS

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    1. D. P. Gaver, 1966. "Observing Stochastic Processes, and Approximate Transform Inversion," Operations Research, INFORMS, vol. 14(3), pages 444-459, June.
    2. Metzler, Ralf & Glöckle, Walter G. & Nonnenmacher, Theo F., 1994. "Fractional model equation for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 13-24.
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    Cited by:

    1. Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
    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. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.

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