During the tertiary stage of oil recovery, various chemicals and gases are injected into the reservoir. The success of these processes often depend on the ability of the injected chemicals/gases making contact with the residual hydrocarbon. The accessibility of the individual pore, where the hydrocarbon are trapped, to the injected fluid is therefore important. In many core flooding experiments which simulate such tertiary processes, the effluent profiles of the injected chemical often exhibit the capacitance effect of early breakthrough and long tails. These are mainly due to the fact that not all the pores are accessible to the displacing fluid. In this work, a mass transfer model, using physical meaningful parameters, has been set up to study the capacitance effect. The pore space are divided into a flowing fraction in which the bulk flow of the injected chemical takes place and a stagnant fraction where the chemical can only access by molecular diffusion. The significance and sensitivity of the five model parameters have been studied extensively using computer simulation. The extent of the mass transfer process is characterised by the different sets of family curves. A series of IPA/water miscible displacements using Clashach sandstone have been carried out to provide experimental data for model simulation. The assumption of the stagnant fraction in the form of dead end pores has been supported by the results of hexane/toluene displacements at connate water saturation. Some problems of history matching the experimental results by model simulation have been highlighted. This is mainly caused by the difficulty of establishing an analytical solution for the model equation and the need to optimise simultaneously the five model parameters. Various approach to overcome these problems have been successfully demonstrated in this work and further possible improvement has been identified. The source of numerical dispersion and the different corrective schemes proposed in various papers have been summarised and compared. One of these, the method of lines (MOL) has been used successfully in this work to minimise numerical dispersion. The understanding of the non-equilibrium capacitance effect in porous media is essential in order to interpret the production data and, in particular, laboratory core flooding results correctly. It is also important, for the mathematical model, to use parameters which are physically meaningful to the process itself. The work carried out in this research has provided a detailed study on this subject.