The effect of small-and intermediate-scale heterogeneities on miscible displacements is investigated by Monte Carlo simulations in a two-dimensional (2D) flow field containing random permeabilities and random layering. The effect of the variable layer lengths on the level of dispersion is calculated for various well-to-well distances. It was determined that the variable layer lengths add a significant amount of dispersion compared with constant layer lengths for well-to-well distances on the order of 1,000 ft [305 m] or less.
IntroductionIn a reservoir engineering study of an oil field, an accurate, detailed description of the reservoir-i.e., permeabilities, porosities, and heterogeneities such as variations in permeabilities, porosities, layering, faults, fractures, and shale streaks-is required. In the past, reservoir descriptions used in simulations contained oversimplified geological models that in many cases described the reservoir as a vertical sequence of homogeneous layers or blocks that extended over very long distances, perhaps even over the entire flow field. This situation was created partially by the need to discretize the porous medium into a limited number of gridblocks for the numerical model and partially from a lack of understanding of the importance of various scales of heterogeneities on the oil recovery and displacement processes. In general, very large-scale features, such as faults and shale layers, would be incorporated in the numerical description, but most intermediate-and small-scale heterogeneities would be omitted. l In many cases, this approximation creates a large error source in the simulation results. The standard technique to reduce this error was to adjust the input data, permeabilities, porosities, relative permeabilities, and other data during history matching, provided that history exists. The trial-anderror history-matching process produces a nonunique reservoir description that has only a small likelihood of accurately predicting future production. The ability of the history-matched model to predict the future is highly dependent on the quality and quantity of the data in the reservoir description, on the detail of the numerical grid, and on the engineer's (who is doing the history match) understanding of the physics, fluid flow, and interactions involved in the particular oil recovery process.To reduce the errors created by simplified descriptions, researchers in the oil industry have recently been describing rock heterogeneities by measuring permeability variations in outcrops and thus attempting to understand reservoir heterogeneities and their effect on oil recovery. 2-4 The assumption is, of course, that the variations and patterns seen in outcrops maintain the same or similar relationships at depth (in oil reservoirs). The next step, after measuring the permeability variations in rock formations, is to determine what effects these descriptions would have on a displacement process. This can generally be accomplished by numerically simulating the displacement process th...