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

Author

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  • 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
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    References listed on IDEAS

    as
    1. 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.
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    3. Efstathios Avdis & Ward Whitt, 2007. "Power Algorithms for Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 341-355, August.
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