Determination of REV and Effective Properties of Fluvial Depositional Systems

Abstract

Fluvial reservoirs are difficult to model due to the high permeability contrast between the sandstone bodies and the overbank deposits and the complex geometry of the permeable (sandstone bodies) and impermeable zones (overbank deposits). A set of fluvial meandering models has been generated using FLUMY. The models represent a range of Net-to-Gross ratios and sandstone body geometries. In order to quantify the effect of sample size on effective properties, the models are evaluated based on the statistical moments of the probability distributions of porosity and single-phase permeability as a function of sample size. The porosity and permeability show a high spread at small sample volumes, but the spread reduces as the sample size increases. A normalized standard deviation, the coefficient of variation, has been used as a criterion for the variability of the probability distributions. The coefficient of variation of the porosity and the horizontal permeability show a monotonic decline as a function of sample size. The coefficient of variation of the vertical permeability does not show a monotonic decline. This is caused by a drastic decrease of the mean of the vertical permeability with increasing sample volume. The mean of the horizontal permeability also decreases with increasing sample size, but to a lesser extent. The mean of the probability distributions of permeability as a function of sample size converges much earlier than the standard deviation. This convergence indicates that we can determine the effective properties at the Representative Elementary Volume (REV), without reaching REV. The convergence of the mean could potentially be used as a criterion for the relevant spatial scale of upscaling from the fine scale static model to the coarse scale model. Furthermore, if cells are uncorrelated at a scale where the mean of the permeability is not a function of sample volume anymore, random attribution of properties can be used to populate dynamic grid cells.