IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v12y2018i1p29-d192650.html
   My bibliography  Save this article

Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift

Author

Listed:
  • Lateef T. Akanji

    (Division of Petroleum Engineering, School of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UK)

  • Gabriel K. Falade

    (Department of Petroleum Engineering, University of Ibadan, Ibadan 23402, Nigeria)

Abstract

A new closed-form analytical solution to the radial transport of tracers in porous media under the influence of linear drift is presented. Specifically, the transport of tracers under convection–diffusion-dominated flow is considered. First, the radial transport equation was cast in the form of the Whittaker equation by defining a set of transformation relations. Then, linear drift was incorporated by considering a coordinate-independent scalar velocity field within the porous medium. A special case of low-intensity tracer injection where molecular diffusion controls tracer propagation but convection with linear velocity drift plays a significant role was presented and solved in Laplace space. Furthermore, a weak-form numerical solution of the nonlinear problem was obtained and used to analyse tracer concentration behaviour in a porous medium, where drift effects predominate and influence the flow pattern. Application in enhanced oil recovery (EOR) processes where linear drift may interfere with the flow path was also evaluated within the solution to obtain concentration profiles for different injection models. The results of the analyses indicated that the effect of linear drift on the tracer concentration profile is dependent on system heterogeneity and progressively becomes more pronounced at later times. This new solution demonstrates the necessity to consider the impact of drift on the transport of tracers, as arrival times may be significantly influenced by drift intensity.

Suggested Citation

  • Lateef T. Akanji & Gabriel K. Falade, 2018. "Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift," Energies, MDPI, vol. 12(1), pages 1-29, December.
    • Handle: RePEc:gam:jeners:v:12:y:2018:i:1:p:29-:d:192650
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/12/1/29/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/12/1/29/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D. P. Gaver, 1966. "Observing Stochastic Processes, and Approximate Transform Inversion," Operations Research, INFORMS, vol. 14(3), pages 444-459, June.
    2. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    3. Efstathios Avdis & Ward Whitt, 2007. "Power Algorithms for Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 341-355, August.
    Full references (including those not matched with items on IDEAS)

    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. A. Baykal Hafızoğlu & Esma S. Gel & Pınar Keskinocak, 2013. "Expected Tardiness Computations in Multiclass Priority M / M / c Queues," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 364-376, May.
    2. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    3. Efstathios Avdis & Ward Whitt, 2007. "Power Algorithms for Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 341-355, August.
    4. Ibrahim Ayuba & Lateef T. Akanji & Jefferson L. Gomes & Gabriel K. Falade, 2021. "Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media," Mathematics, MDPI, vol. 9(19), pages 1-36, October.
    5. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
    6. Jonathan K. Budd & Peter G. Taylor, 2015. "Calculating optimal limits for transacting credit card customers," Papers 1506.05376, arXiv.org, revised Aug 2015.
    7. Dassios, Angelos & Lim, Jia Wei, 2013. "Parisian option pricing: a recursive solution for the density of the Parisian stopping time," LSE Research Online Documents on Economics 58985, London School of Economics and Political Science, LSE Library.
    8. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    9. Feng, Runhuan & Volkmer, Hans W., 2012. "Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 409-421.
    10. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    11. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    12. Kimura, Toshikazu, 2008. "Valuing finite-lived Russian options," European Journal of Operational Research, Elsevier, vol. 189(2), pages 363-374, September.
    13. Chenxu Li, 2016. "Bessel Processes, Stochastic Volatility, And Timer Options," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 122-148, January.
    14. Blanc, J.P.C., 2001. "On the Numerical Inversion of Busy-Period Related Transforms," Other publications TiSEM 6c859c40-8d0b-4b3b-9526-a, Tilburg University, School of Economics and Management.
    15. Richard L. Warr & Cason J. Wight, 2020. "Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 881-904, September.
    16. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    17. He, Gang & Wu, Wenqing & Zhang, Yuanyuan, 2018. "Analysis of a multi-component system with failure dependency, N-policy and vacations," Operations Research Perspectives, Elsevier, vol. 5(C), pages 191-198.
    18. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    19. David H Collins & Richard L Warr & Aparna V Huzurbazar, 2013. "An introduction to statistical flowgraph models for engineering systems," Journal of Risk and Reliability, , vol. 227(5), pages 461-470, October.
    20. Gatto, Riccardo, 2013. "The von Mises–Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1669-1676.

    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:gam:jeners:v:12:y:2018:i:1:p:29-:d:192650. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.