A030 UNCERTAINTY QUANTIFICATION FOR MATURE FIELD COMBINING THE BAYESIAN INVERSION FORMALISM AND EXPERIMENTAL DESIGN APPROACH

The goal of a reservoir study is to help to decide the future development of a field based on technical and economic criteria. To reach this goal, one would like to quantify the impact of uncertainty on production and economic forecasts to take the decision while considering the risk. Practically it would correspond to supply to the manager the uncertainty distribution (or P10, 50 and 90) of the production forecasts associated to each scenario. The uncertainty on the production forecasts is linked to a specific scenario and to the knowledge of the reservoir. For a mature field two kinds of knowledge exist: - Static parameters used to build the numerical model: geological concept, variograms, correlation lengths, permeability and porosity distributions, etc. The static parameters are associated with "a priori uncertainties" defined by their probability distributions. - Dynamic data: measurements related to the dynamic behavior of the reservoir, such as measured pressure, oil/water/gas rates at the wells, 4d seismic, etc. The bayesian formalism enables to reduce, in a statistical framework, the static parameter uncertainties by taking into account the dynamic data. These "a posteriori" distributions of the static parameters can then be used to compute probabilistic production forecasts for each possible scenario honoring static and dynamic knowledge of the reservoir. However, this formalism involves the determination of the likelihood function, which can lead to a prohibitive cost in terms of reservoir simulations. To drastically decrease the amount of reservoir simulations needed to determine the "a posteriori" uncertainties we propose to approximate the likelihood function by a non-linear proxy model combining experimental design, universal kriging and dynamic training techniques. These "a posteriori" distributions can then be used into the classical experimental design approach to compute probabilistic production forecasts constrained by dynamic data. The proposed methodology will be illustrated on a field case.