Simulations of flow and transport in highly heterogeneous porous formations: Numerical issues

Large-scale numerical simulations were conducted to investigate the stationarity and ergodicity requirements for modeling flow and transport in highly heterogeneous formations. The size of the flow domain was in the excess of 1200 integral scales of log-conductivity in 2. D and 200 in 3. D. Results show that the velocity field is nonstationary only within a narrow band along the boundary (less that 5 integral scales wide). The domain sizes that are required to obtain stable, ergodic results for the longitudinal macrodispersivity using a single realization of a medium are large and they increase dramatically with log-conductivity variance: the required sizes are in the excess of 500 integral scales for log-conductivity variance of 8 in 2D. All 3. D simulations conducted here with variance of 4 were likely non-ergodic.