Ensemble Based Data Assimilation to Reduce Hierarchical Architectural and Structural Uncertainties on Real Geomodels

3D distribution of petrophysical parameters (porosity, permeability, relative permeability coefficient, etc) constitutes one of the key reservoir uncertainties. Facies are commonly used as high order controls for petrophysical parameters. While the petrophysical characteristics of each facies can be evaluated at wells, their spatial distribution is very often poorly known, typically derived only from indirect means (such as 3D seismic). This makes the distribution of different facies type in the reservoir model one of the important (if not the main) sources of uncertainty. Of particular importance are the discrete petrophysical properties such as relative permeability tables that are often directly linked to facies.

Facies are not the only categorical parameters in a complex geomodel and normally there is a hierarchy to follow from architectural elements, to facies, rocktypes and finally petrophysical values. Apart from the lowest level of parameters in this hierarchy the rest are discrete and often non-sort-able parameters. As a consequence, adjusting their uncertainty with a methodology like ensemble Kalman filter is not straightforward. Simply assimilating on discrete values there is a high probability of finding non discrete ones which won’t be obvious to associate to the reservoir cells.

Level set methodology proposed in ( Lorentzen et. al. 2011 ) to address this issue and calculate the closest distance to the boundary of facies which has been elaborated by benefiting from variogram information ( Abadpour et al. 2013 ) deployed in this work to address the uncertainty on above mentioned four level of hierarchy (architectural elements, facies, rocktypes and petrophysical parameters in multi realization of geomodels) on top of grid structural uncertainties of a real reservoir model with a synthetic production profile.

After achieving a satisfactory match quality and harmonious final realizations the ensemble of posterior models has been challenged from the geostatistical and geological point of view to show the validity of the process. Furthermore geological and geostatistical biases has been also introduced in the prior models to evaluate the capacity of the filtering technique to reach the truth model via inverse procedure.