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Solute dispersion in a porous formation is Mathematically expressed by partial differential equation well known as advection-dispersion equation (ADE). The present study deals with the solute transport governing equation in a semi-infinite homogeneous porous formation under linear sorption. A constant background solute concentration is assumed initially throughout the solute transport domain. Dirichlet and Neumann type boundary conditions are considered to examine the solute concentration distribution profile in the semi-infinite porous medium. The analytical and numerical solutions of the model problem are derived by Laplace transform technique and Crank-Nicolson method, respectively. Solute dispersion behaviour is studied for various form of flow velocities. Solutions obtained by analytical and numerical techniques are illustrated graphically with the help of MATLAB software. Also, the numerical solution is compared with the analytical solution and found great similarity between them.

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