MODELING FLOW IN HETEROGENEOUS MEDIA USING STREAMTUBES .1. MISCIBLE AND IMMISCIBLE DISPLACEMENTS

We present a rapid numerical technique for modeling convective displac ements that are dominated by large-scale heterogeneities. Streamtubes map the direction of flow at any time during the displacement and are re-calculated as the fluid mobility distribution changes. Two-dimensio nal solutions are then constructed by mapping one-dimensional solution s along each streamtube. The novel feature of our technique is the use of one-dimensional solutions along changing streamtubes. The solution at a new time level is given as an integration from 0 to t + Delta t, rather than from t to t + t Delta t, as in standard timestepping algo rithms. Our method allows large timesteps to be taken, producing stabl e, diffusion-free solutions in a fraction elf the time taken by conven tional finite-difference/finite-element simulators, thereby permitting a statistical approach to reservoir forecasting.