Spatial modeling of heterogeneous initial water saturation

This paper proposes the stochastic modeling of initial water saturation in reservoirs to improve the computation of static water volume using three-dimensional cellular models. The spatial summation after multiplying each cell volume by its porosity and water saturation to evaluate fluid content is developed from perturbation analysis which proves that static saturation models must observe non-linear correlations and heterogeneity patterns. The relation between water saturation and a J function is derived using an exponential relation. A consequence of heterogeneity in the exponential model is that spatial modeling of initial water saturation should be done using vertical non-stationary random field models which allow handling the capillary effect and variable correlation. Particular emphasis is devoted to a stationary component of saturation correlated to porosity. The spatial stochastic methodology provided in this paper is implemented stepwise by considering the variability due to capillarity with J functions acknowledging the correlation of petrophysical properties and water saturation from laboratory and logging data. Stochastic spatial saturation models resulting from this methodology may impact the assessment of the initial volume of fluids in transition zones above free water level.