Designing Optimal Data Acquisition Schemes Using Kullback-Leibler Divergence within the Bayesian Framework

Oil and gas reservoirs are commonly complex heterogeneous natural structures that are described by means of several direct or indirect field measurements involving different physical processes operating at different spatial and temporal scales. Seismic techniques provide a description of the large scale geological structures. In some cases, they can help to characterize the spatial fluid distribution, which knowledges can in turn be used to improve the oil recovery strategy. In practice, these measurements are always expensive and due to their indirect, local and incomplete nature, an exhaustive representation of the entire reservoir cannot be attained. Several uncertainties are always remaining, that must be conveniently propagated in the modeling workflow to deduce in turn uncertainties of the production forecasts. Those uncertainties are essential when setting up a reservoir development scenario. A typical issue is to choose between several oil recovery scenario, or position and trajectory of a new well. Due to the cost of the associated field operations, it is essential to model the risks due to the remaining uncertainties. It is within this framework that devising strategies allowing to set-up optimal data acquisition schemes can have many applications in oil or gas reservoir engineering, or in the recently considered CO2 geological storages involving analogous technologies. We present a method allowing us to quantify the information that is potentially provided by any set of measurements. Applying a Bayesian framework, we quantify the information content of any set of data using the so called Kullback-Leibler divergence between posterior and prior distributions. In the case of a gaussian model where the data depend linearly on the parameters, analytic formulae are given and allow us to define the optimal set of time acquisitions. The redundancy of information can also be quantified, highlighting the role of the correlation structure of the prior model.