Abstract The field of numerical reservoir simulation has become one of the fastest growing bodies of knowledge over the past two decades, because of the strong demand for reliable predictions of reservoir performance. The tremendous progress in electronic computing hardware, and the significant improvement in methods of numerical analysis were two important factors in the achievements made in numerical models of reservoirs. Such models made important contributions to the enhanced oil recovery of light and medium oils. Heavy oil development is one of the major concerns for the oil industry in the eighties. Its recovery is associated with some of the most complex thermal processes. The demand Jar reliable software capable of producing useful predictions of heavy oil recovery requires further development in numerical methods of reservoir simulation. There are a number of areas which need further research. Some of these areas are described in this paper. Possible directions Of study are also indicated. It is shown that numerical dispersion and stability constitutes a problem which needs some imaginative solution. Modelling of the immediate neighbourhood of a well, and modelling at the physico-chemical processes in a single grid block are also areas f difficulties in reservoir simulation. Introduction Over the past two decades, numerical simulation developed into a strong predictive tool in the oil industry. With the advent of powerful electronic computers, numerical simulation became an important approach, which is complementary to laboratory experimentation. The development of reservoir oil simulators was enhanced by a number of advantages:Computer simulation is generally an economical way of experimentation and pilot testing.It has the experimental capability of discovery of phenomena. Executing computations under varied values of parameters may lead to discoveries, usually unknown otherwise.It provides instant computer control over the parameters of an oil field which have been adequately incorporated in the model, thus providing unlimited resources of experimentation.It has the ability to conduct tests of parameter sensitivity which are unthinkable in laboratory conditions.An existing model can be used to solve numerous daily field problems during the lifetime of recovery. Conventional light oil reservoirs with low-viscosity oil systems, consisting mainly of methane and heavy components, have been well served by the so-called black-oil models. These models account for only three components; oil, gas, and water. The simplifying assumptions state that the oil component can exist only in the oil phase, that the gas component can exist in both gas and oil phases, and that the water component can exist only in the water phase. In other words the black -oil models are based only on fluid-mechanics and total mass conservation law. They ignore mass transfer, heat energies, phase changes and chemical reactions. At a later stage the compositional approach to reservoir simulation was developed to account for some of these factors, when they affect recovery processes. A compositional odel considers the hydrocarbon phases as a mixture of some N-components. These components could be methane, ethane, etc.