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A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs

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Listed:
  • Chang, Ailian
  • Sun, HongGuang
  • Zheng, Chunmiao
  • Lu, Bingqing
  • Lu, Chengpeng
  • Ma, Rui
  • Zhang, Yong

Abstract

Fractional-derivative models have been developed recently to interpret various hydrologic dynamics, such as dissolved contaminant transport in groundwater. However, they have not been applied to quantify other fluid dynamics, such as gas transport through complex geological media. This study reviewed previous gas transport experiments conducted in laboratory columns and real-world oil–gas reservoirs and found that gas dynamics exhibit typical sub-diffusive behavior characterized by heavy late-time tailing in the gas breakthrough curves (BTCs), which cannot be effectively captured by classical transport models. Numerical tests and field applications of the time fractional convection–diffusion equation (fCDE) have shown that the fCDE model can capture the observed gas BTCs including their apparent positive skewness. Sensitivity analysis further revealed that the three parameters used in the fCDE model, including the time index, the convection velocity, and the diffusion coefficient, play different roles in interpreting the delayed gas transport dynamics. In addition, the model comparison and analysis showed that the time fCDE model is efficient in application. Therefore, the time fractional-derivative models can be conveniently extended to quantify gas transport through natural geological media such as complex oil–gas reservoirs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:502:y:2018:i:c:p:356-369
    DOI: 10.1016/j.physa.2018.02.080
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    References listed on IDEAS

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    1. Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J. & Alvarez-Ramirez, Jose, 2007. "On the effective viscosity for the Darcy–Brinkman equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 69-79.
    2. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    3. Holloway, S., 2005. "Underground sequestration of carbon dioxide—a viable greenhouse gas mitigation option," Energy, Elsevier, vol. 30(11), pages 2318-2333.
    4. Li, Wei & Li, Can, 2015. "Second-order explicit difference schemes for the space fractional advection diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 446-457.
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    Cited by:

    1. 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.
    2. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    3. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.

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