History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

The Ensemble Kalman Filter (EnKF) has been successfully applied in petroleum engineering during the past few years to constrain reservoir models to production or seismic data. This sequential assimilation method provides a set of updated static variables (porosity, permeability) and dynamic variables (pressure, saturation) at each assimilation time. However, several limitations can be pointed out. In particular, the method does not prevent petrophysical realizations from departing from prior information. In addition, petrophysical properties can reach extreme (non-physical) values. In this work, we propose to combine the EnKF with two parameterization methods designed to preserve second-order statistical properties: pilot points and gradual deformation. The aim is to prevent the departure of the constrained petrophysical property distributions from prior information. Over/under estimations should also be avoided. The two algorithms are applied to a synthetic case. Several parameter configurations are investigated in order to identify solutions improving the performance of the method.

► We propose two algorithms to combine EnKF with Pilot point and Gradual Deformation.
► The goal is to honor prior data and avoid unphysical values in EnKF applications.
► Algorithm 1 performs better by more and better positioned pilot points.
► Algorithm 2 performs better by a larger background ensemble and local deformation.
► Both algorithms are applied to a two dimensional synthetic reservoir case study.