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.
Highlights
The study of the transport of tracers has become an essential technique for porous media characterisation, in enhanced oil recovery (EOR) in hydrocarbon reservoirs (e.g., Baldwin [1]), hydrology (e.g., Rubin and James [2]), nuclear (e.g., Moreno et al [3] and Herbert et al [4]), drug transport in blood vessels (e.g., Mabuza et al [5]) and geothermal engineering (e.g., Vetter and Zinnow [6]).Multiple processes and mechanisms are usually involved in the chemical interaction of the constituent components when the tracer is being transported through a porous medium
Despite the extensive research in this field, in solving the advection–dispersion equation (ADE) both analytically and numerically, there is yet to be a consideration for the closed-form solution of the ADE
The transport of tracers in a constant flow of carrier fluid flowing in a porous medium governed by the convection–diffusion equation expressed in terms of resident concentration in radial coordinates can be written as : 1 ∂
Summary
The study of the transport of tracers has become an essential technique for porous media characterisation, in enhanced oil recovery (EOR) in hydrocarbon reservoirs (e.g., Baldwin [1]), hydrology (e.g., Rubin and James [2]), nuclear (e.g., Moreno et al [3] and Herbert et al [4]), drug transport in blood vessels (e.g., Mabuza et al [5]) and geothermal engineering (e.g., Vetter and Zinnow [6]). Applied Fourier series methods to numerically solve the Laplace transform of a pressure distribution equation for radial flow in porous media. Despite the extensive research in this field, in solving the advection–dispersion equation (ADE) both analytically and numerically, there is yet to be a consideration for the closed-form solution of the ADE in systems where the effect of linear drift may predominate. In cases where hydrodynamic dispersion is radially distributed and linear drift predominates, an exact analytical solution to the transport equation has not been reported in the literature. A weak-form numerical solution is obtained and used to analyse tracer concentration behaviour in enhanced oil recovery (EOR) processes where linear drift effect may interfere with the fluid flow path
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