Abstract Streamline techniques offer the possibility of high speed reservoir simulation, but existing methods have some limitations for example, the pressure field is frequently derived using the assumption of incompressible flow. Unlike conventional simulation, material conservation is not inherent in the method, but can act as a check on the accuracy obtained. Using a pressure equation based on molar density variables, we extend the streamline technique to handle compressibility and depletion. The streamline update then becomes an alternative method of updating the composition field to the usual conservation equations. By using and comparing both methods we can assess the accuracy and speed gains obtained using the streamline approach. The treatment of wells is an area of interest in streamline simulation. When a number of streamlines enter a producer cell the contribution from each must be weighted carefully, as this defines the solution in the vicinity of the well and the composition of the produced fluid. It should also be possible for fluids to pass through a well completion cell without being produced, for example in the vicinity of a strong aquifer. In order to treat near well effects in detail, we combine a streamline model for the bulk of the reservoir with a more general model near the well. P. 273