Measurement Of Physical Dispersion In Random Correlated Permeability Fields And Its Application For Upscaling

An algorithm is developed to measure local dispersion within the model. The algorithm is based on solving the solution of convective-diffusive equation between two neighbouring cells in a 1D model to identify the relevant Peclet number describing dispersion between them. The algorithm may be applied for the entire pair of grid blocks located in the transition zone; for each pair of grid blocks a Peclet number may be measured. Properly averaging these measured Peclet numbers could provide an estimate of the total system dispersion coefficient. Measurement of dispersion in systems with known numerical and physical dispersions also confirmed algorithm's accuracy. The algorithm is later applied to 2D heterogeneous random correlated permeability fields. As with the 1D model, measurement of Peclet numbers may be carried out between all pair of neighbouring cells located only in the transition zone for either horizontal or vertical orientations. This in turn provide estimate regarding dispersion coefficient for that respective orientations. For each respective orientation, the measured dispersion coefficients can be matched with equivalent numerical grid block sizes replicating the same physical mixing. This provides a rapid tool for estimating the approximate number of grid blocks for different orientations particularly for a miscible simulation.