The main focus of the present research work has been the development of a multi-scale finite element modelling technique for transport phenomena. Initially the isothermal steady flow of a Newtonian fluid through highly permeable porous media has been modelled and then the method is extended to more complex problems such as the convection-diffusion equation. The standard Galerkin method is used to model the flow in highly permeable porous media and, considering the disadvantages of this method the focus of study is moved to methods which can deal with multi-scale problems. Two-dimensional models based on both the continuous penalty method and the mixed method using the Taylor-Hood element are applied. The Brinkman model together with the continuity equation are used to simulate the flow in highly permeable porous media. In addition to the no-slip wall boundary conditions, the Navier's slip wall boundary conditions has been used in conjunction with the Brinkman equation to make it possible to apply this equation at low permeability.