Abstract
This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, a weak-form solution of radial transport of tracers under convection–diffusion-dominated flow is established using hypergeometric functions. The velocity field associated with the radial transport is informed by the solution of the Stokes equations. Channel thickness as a function of velocities, maximum Reynolds number of each thickness as a function of maximum velocities and concentration profile for different drift and dispersion coefficients are computed and analysed. Analysis of the simulation results reveals that the dispersion coefficient appears to be a significant factor controlling the concentration distribution of the tracer at pore scale. Further analysis shows that the drift coefficient appears to influence tracer concentration distribution but only after a prolonged period. This indicates that even at pore scale, tracer drift characteristics can provide useful information about the flow and transport properties of individual pores in porous media.
Highlights
A thorough understanding of transport processes is significant for various applications in engineering, natural resources groundwater remediation [2] and porous media during tracer injection experiments in a core samples [3].Tracer testing has become a highly vital tool in geothermal research, resource management and development
The convective velocity of the fluid due to transport at pore scale is described by the Poiseuille velocity calculated from Equation (3) above which decomposes into drift velocity and a radial velocity part of an injected tracer of strength qi around the drift velocity
The results show that the effect of drift on concentration distribution appears at a later time for a variable dispersion coefficient
Summary
A thorough understanding of transport processes is significant for various applications in engineering, natural resources (for example waste management [1]) groundwater remediation [2] and porous media during tracer injection experiments in a core samples [3]. Studies have shown that porous media in which transport takes place are heterogeneous and disordered on a microscopic scale, higher additional mixing is required by order of magnitude than the spreading due to pure molecular diffusion Such an increase in the spreading of an initially narrow tracer pulse is due to mechanical dispersion. The advection–diffusion equation is a standard approach based on Ficks law and the conservation of mass It assumes Fickian processes and uses hydrodynamic dispersion coefficient in which the effect of solute mixing and spreading are embedded together [3]. Concentration distribution around the source of the tracer or injected particles is computed from a weak-form numerical solution and used to analyse pore-scale tracer concentration behaviour in tracer injection/extraction experiment in a core sample during enhanced oil recovery processes where the influence of drift may obstruct the fluid flow path
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