Analytical solution for solute transport of tracer injection in anisotropic media
A three-dimensional (3-D) analytical model for tracer injection can be a valuable tool to inspect solute transport in anisotropic porous media. Analytical solutions mostly derived using Laplace transform with appropriate initial and boundary conditions are generally used to provide limited isotropic parameters in 1-D or 2-D with natural flow. Nowadays, researchers attempt to combine tracer test analysis with anisotropic 3-D numerical models to construct realistic reservoir models in which use of isotropic parameters are mostly inadequate. In this study, the Green’s function method, which is quite efficient to tackle different boundary and initial conditions in multi-dimensional problems, is applied to facilitate a moving line-source solution of the convection-dispersion-diffusion equation for solute transport in 3-D uniform porous medium. Moreover, the Green’s function equation is analytically convoluted with a rectangular pulse function, which represents tracer injection. This provides additional flexibility to apply multiple tracer injections in a given time span. Results demonstrate that the novel analytical model provides robust evaluations to determine required parameters such as flow velocities, longitudinal and transversal dispersivities in complex reservoir systems with anisotropic flow paths.