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Energies 2019, 12(1), 29; https://doi.org/10.3390/en12010029

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

1
Division of Petroleum Engineering, School of Engineering, University of Aberdeen, Aberdeen AB24 3FX, UK
2
Department of Petroleum Engineering, University of Ibadan, Ibadan 23402, Nigeria
*
Author to whom correspondence should be addressed.
Received: 3 November 2018 / Revised: 10 December 2018 / Accepted: 17 December 2018 / Published: 22 December 2018
(This article belongs to the Special Issue Sustainability of Fossil Fuels)
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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. View Full-Text
Keywords: transport of tracers; linear drift effect; convection–diffusion equation; enhanced oil recovery; closed-form analytical solution transport of tracers; linear drift effect; convection–diffusion equation; enhanced oil recovery; closed-form analytical solution
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Akanji, L.T.; Falade, G.K. Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift. Energies 2019, 12, 29.

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