An Analytical Solution for an Exponential- Type Dispersion Process

The dispersion process in heterogeneous porous media is distance-dependent,which results from multi-scaling property of heterogeneous structure.An analytical model describing the dispersion with an exponential dispersion function is build,which is transformed into ODE problem with variable coefficients,and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique.Acoording to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed.