IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v502y2018icp356-369.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118301560
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.02.080?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emad A. Al‐Khdheeawi & Stephanie Vialle & Ahmed Barifcani & Mohammad Sarmadivaleh & Stefan Iglauer, 2017. "Influence of CO 2 ‐wettability on CO 2 migration and trapping capacity in deep saline aquifers," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 7(2), pages 328-338, April.
    2. Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    3. Qu, Hai-Dong & Liu, Xuan & Lu, Xin & ur Rahman, Mati & She, Zi-Hang, 2022. "Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Valentina Bosetti & Laurent Gilotte, 2005. "Carbon Capture and Sequestration: How Much Does this Uncertain Option Affect Near-Term Policy Choices?," Working Papers 2005.86, Fondazione Eni Enrico Mattei.
    5. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    6. Anita Punia, 2021. "Carbon dioxide sequestration by mines: implications for climate change," Climatic Change, Springer, vol. 165(1), pages 1-17, March.
    7. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. 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.
    9. Tabatabaei, S. Sepehr & Talebi, H.A. & Tavakoli, M., 2017. "A novel adaptive order/parameter identification method for variable order systems application in viscoelastic soft tissue modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 447-455.
    10. Hamid, M. & Usman, M. & Haq, R.U. & Wang, W., 2020. "A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    11. Zahra, Waheed K. & Abdel-Aty, Mahmoud & Abidou, Diaa, 2020. "A fractional model for estimating the hole geometry in the laser drilling process of thin metal sheets," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    12. Hu, Haixiang & Li, Xiaochun & Fang, Zhiming & Wei, Ning & Li, Qianshu, 2010. "Small-molecule gas sorption and diffusion in coal: Molecular simulation," Energy, Elsevier, vol. 35(7), pages 2939-2944.
    13. Piotr Słomski & Maria Mastalerz & Jacek Szczepański & Arkadiusz Derkowski & Tomasz Topór & Marcin Lutyński, 2020. "Experimental and numerical investigation of CO2–brine–rock interactions in the early Palaeozoic mudstones from the Polish part of the Baltic Basin at simulatedin situ conditions," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 10(3), pages 567-590, June.
    14. Labus, Krzysztof & Bujok, Petr, 2011. "CO2 mineral sequestration mechanisms and capacity of saline aquifers of the Upper Silesian Coal Basin (Central Europe) - Modeling and experimental verification," Energy, Elsevier, vol. 36(8), pages 4974-4982.
    15. Alshammari, Yousef M. & Sarathy, S. Mani, 2017. "Achieving 80% greenhouse gas reduction target in Saudi Arabia under low and medium oil prices," Energy Policy, Elsevier, vol. 101(C), pages 502-511.
    16. Meng, Ruifan & Yin, Deshun & Yang, Haixia & Xiang, Guangjian, 2020. "Parameter study of variable order fractional model for the strain hardening behavior of glassy polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    17. Procesi, M. & Cantucci, B. & Buttinelli, M. & Armezzani, G. & Quattrocchi, F. & Boschi, E., 2013. "Strategic use of the underground in an energy mix plan: Synergies among CO2, CH4 geological storage and geothermal energy. Latium Region case study (Central Italy)," Applied Energy, Elsevier, vol. 110(C), pages 104-131.
    18. Beining Zhang & Weiguo Liang & Pathegama Gamage Ranjith & Wei He & Zhigang Li & Xiaogang Zhang, 2018. "Effects of Coal Deformation on Different-Phase CO 2 Permeability in Sub-Bituminous Coal: An Experimental Investigation," Energies, MDPI, vol. 11(11), pages 1-25, October.
    19. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    20. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:502:y:2018:i:c:p:356-369. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.